Method and apparatus for video coding

ABSTRACT

A method for video decoding in a decoder is provided. In the method, transform block signaling information is acquired from a coded video bitstream. A transform type is determined based on the transform block signaling information. A low frequency coefficient of one of a plurality of sub transform units is determined based on the transform type and neighboring sub transform units of the one of the plurality of sub transform units. The plurality of sub transform units is partitioned from a current coding block unit (CU). The current coding block unit is subsequently decoded based on low frequency coefficients of the plurality of sub transform units, where the low frequency coefficients include the low frequency coefficient of the one of the plurality of sub transform units.

INCORPORATION BY REFERENCE

This present application claims the benefit of priority to U.S.Provisional Application No. 62/819,568, “DC PREDICTION FOR SUB TRANSFORMUNIT” filed on Mar. 16, 2019. The entire disclosures of the priorapplications are hereby incorporated by reference in their entirety.

TECHNICAL FIELD

The present disclosure describes embodiments generally related to videocoding.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Video coding and decoding can be performed using inter-pictureprediction with motion compensation. Uncompressed digital video caninclude a series of pictures, each picture having a spatial dimensionof, for example, 1920×1080 luminance samples and associated chrominancesamples. The series of pictures can have a fixed or variable picturerate (informally also known as frame rate), of, for example 60 picturesper second or 60 Hz. Uncompressed video has significant bitraterequirements. For example, 1080p60 4:2:0 video at 8 bit per sample(1920×1080 luminance sample resolution at 60 Hz frame rate) requiresclose to 1.5 Gbit/s bandwidth. An hour of such video requires more than600 gigabytes (GB) of storage space.

One purpose of video coding and decoding can be the reduction ofredundancy in the input video signal, through compression. Compressioncan help reduce the aforementioned bandwidth or storage spacerequirements, in some cases by two orders of magnitude or more. Bothlossless and lossy compression, as well as a combination thereof can beemployed. Lossless compression refers to techniques where an exact copyof the original signal can be reconstructed from the compressed originalsignal. When using lossy compression, the reconstructed signal may notbe identical to the original signal, but the distortion between originaland reconstructed signals is small enough to make the reconstructedsignal useful for the intended application. In the case of video, lossycompression is widely employed. The amount of distortion tolerateddepends on the application; for example, users of certain consumerstreaming applications may tolerate higher distortion than users oftelevision distribution applications. The compression ratio achievablecan reflect that: higher allowable/tolerable distortion can yield highercompression ratios.

A video encoder and decoder can utilize techniques from several broadcategories, including, for example, motion compensation, transform,quantization, and entropy coding.

Video codec technologies can include techniques known as intra coding.In intra coding, sample values are represented without reference tosamples or other data from previously reconstructed reference pictures.In some video codecs, the picture is spatially subdivided into blocks ofsamples. When all blocks of samples are coded in intra mode, thatpicture can be an intra picture. Intra pictures and their derivationssuch as independent decoder refresh pictures, can be used to reset thedecoder state and can, therefore, be used as the first picture in acoded video bitstream and a video session, or as a still image. Thesamples of an intra block can be exposed to a transform, and thetransform coefficients can be quantized before entropy coding. Intraprediction can be a technique that minimizes sample values in thepre-transform domain. In some cases, the smaller the DC value after atransform is, and the smaller the AC coefficients are, the fewer thebits that are required at a given quantization step size to representthe block after entropy coding.

Traditional intra coding such as known from, for example MPEG-2generation coding technologies, does not use intra prediction. However,some newer video compression technologies include techniques thatattempt, from, for example, surrounding sample data and/or metadataobtained during the encoding/decoding of spatially neighboring, andpreceding in decoding order, blocks of data. Such techniques arehenceforth called “intra prediction” techniques. Note that in at leastsome cases, intra prediction is only using reference data from thecurrent picture under reconstruction and not from reference pictures.

There can be many different forms of intra prediction. When more thanone of such techniques can be used in a given video coding technology,the technique in use can be coded in an intra prediction mode. Incertain cases, modes can have submodes and/or parameters, and those canbe coded individually or included in the mode codeword. Which codewordto use for a given mode/submode/parameter combination can have an impactin the coding efficiency gain through intra prediction, and so can theentropy coding technology used to translate the codewords into abitstream.

A certain mode of intra prediction was introduced with H.264, refined inH.265, and further refined in newer coding technologies such as jointexploration model (JEM), versatile video coding (VVC), and benchmark set(BMS). A predictor block can be formed using neighboring sample valuesbelonging to already available samples. Sample values of neighboringsamples are copied into the predictor block according to a direction. Areference to the direction in use can be coded in the bitstream or mayitself be predicted.

SUMMARY

Aspects of the disclosure provide methods and apparatuses for videoencoding/decoding. In some examples, an apparatus for video decodingincludes receiving circuitry and processing circuitry.

According to an aspect of the disclosure, a method for video decoding ina decoder is provided. In the method, transform block signalinginformation is acquired from a coded video bitstream. A transform typeis determined based on the transform block signaling information. A lowfrequency coefficient of one of a plurality of sub transform units isdetermined based on the transform type and neighboring sub transformunits of the one of the plurality of sub transform units. The pluralityof sub transform units is partitioned from a current coding block unit(CU). The current coding block unit is subsequently decoded based on lowfrequency coefficients of the plurality of sub transform units, wherethe low frequency coefficients include the low frequency coefficient ofthe one of the plurality of sub transform units.

In some embodiments, the transform block signaling information caninclude a first high level syntax element, a second high level syntaxelement, or a third high level syntax element. The high level syntaxelement indicates that the transform type is a discrete cosine transform2 (DCT-2). The second high level syntax element indicates that thetransform type is one of the DCT-2 or a transform skip. The third highlevel syntax element indicates that the transform type is a multipletransform selection (MTS) based on a discrete cosine transform 8 (DCT-8)and a discrete sine transform 7 (DST-7).

In some embodiments, the transform block signaling information canindicate that the transform type is a discrete cosine transform 2(DCT-2) when the plurality of sub transform units is partitioned fromthe current coding block unit (CU) by an implicit transform split.

In order to determine the low frequency coefficient, an absolute valueor a signed value of the low frequency coefficient of the one of theplurality of sub transform units can be determined based on transformcoefficients of the neighboring sub transform units of the one of theplurality of sub transform units.

In some embodiments, the absolute value of the low frequency coefficientof the one of plurality of sub transform units can be determined basedon an average of absolute values of low frequency coefficients of a topand/or a left neighboring sub transform units of the one of theplurality of sub transform units. The signed value of the low frequencycoefficient of the one of the plurality of sub transform units can bedetermined based on an average of signed values of low frequencycoefficients of a top and/or a left neighboring sub transform units ofthe one of the plurality of sub transform units.

In some embodiments, absolute values of low frequency coefficients ofneighboring sub transform units can be scaled when the one of theplurality of sub transform units and the neighboring sub transform unitsare transformed based on different transform types.

In some embodiments, the plurality of sub transform units can bepartitioned from the current coding block unit based on at least one ofan Intra Sub-Partitions mode, or an implicit transform split.

In some embodiments, after the low frequency coefficient of the one ofthe plurality of sub transform units is determined, a secondarytransform can be performed on the low frequency coefficients of theplurality of sub transform units to obtain a plurality of transformcoefficients. Each of the plurality of transform coefficients can beobtained based on a corresponding low frequency coefficient of theplurality of sub transform units. Subsequently, the current coding blockunit can be decoded based on the plurality of transform coefficients.

In some embodiments, the secondary transform can include a non-squareHadamard transform, a square Hadamard transform, a DCT-2, a DST-7, aDCT-8, a Karhunen-Loeve Transform (KLT), or a non-separable KLT.

In some embodiments, the secondary transform can be performed when theplurality of sub transform units in the current coding block unit (CU)share a same transform type.

Aspects of the disclosure also provide a non-transitorycomputer-readable medium storing instructions which when executed by acomputer for video decoding cause the computer to perform the method forvideo decoding.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features, the nature, and various advantages of the disclosedsubject matter will be more apparent from the following detaileddescription and the accompanying drawings in which:

FIG. 1 is a schematic illustration of a simplified block diagram of acommunication system (100) in accordance with an embodiment.

FIG. 2 is a schematic illustration of a simplified block diagram of acommunication system (200) in accordance with an embodiment.

FIG. 3 is a schematic illustration of a simplified block diagram of adecoder in accordance with an embodiment.

FIG. 4 is a schematic illustration of a simplified block diagram of anencoder in accordance with an embodiment.

FIG. 5 shows a block diagram of an encoder in accordance with anotherembodiment.

FIG. 6 shows a block diagram of a decoder in accordance with anotherembodiment.

FIG. 7A shows an exemplary block partitioning by using quad-tree plusbinary tree (QTBT).

FIG. 7B shows a corresponding tree representation of the exemplary blockpartitioning by using the QTBT.

FIG. 8A shows a vertical center-side triple-tree partitioning.

FIG. 8B shows a horizontal center-side triple-tree partitioning.

FIG. 9 shows a first exemplary division of a luma intra-predicted blockbased on Intra Sub-Partitions (ISP) coding mode.

FIG. 10 shows a second exemplary division of luma intra-predicted blockbased on Intra Sub-Partitions (ISP) coding mode.

FIGS. 11A-11D show exemplary sub-block transform modes.

FIG. 12 shows an exemplary split of a 64×32 coding unit (CU) into eight16×16 sub transform units (STUs).

FIG. 13 shows a formation of a coefficient block based on a plurality ofSTUs.

FIG. 14 shows a flow chart outlining a process example according to someembodiments of the disclosure.

FIG. 15 is a schematic illustration of a computer system in accordancewith an embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 illustrates a simplified block diagram of a communication system(100) according to an embodiment of the present disclosure. Thecommunication system (100) includes a plurality of terminal devices thatcan communicate with each other, via, for example, a network (150). Forexample, the communication system (100) includes a first pair ofterminal devices (110) and (120) interconnected via the network (150).In the FIG. 1 example, the first pair of terminal devices (110) and(120) performs unidirectional transmission of data. For example, theterminal device (110) may code video data (e.g., a stream of videopictures that are captured by the terminal device (110)) fortransmission to the other terminal device (120) via the network (150).The encoded video data can be transmitted in the form of one or morecoded video bitstreams. The terminal device (120) may receive the codedvideo data from the network (150), decode the coded video data torecover the video pictures and display video pictures according to therecovered video data. Unidirectional data transmission may be common inmedia serving applications and the like.

In another example, the communication system (100) includes a secondpair of terminal devices (130) and (140) that performs bidirectionaltransmission of coded video data that may occur, for example, duringvideoconferencing. For bidirectional transmission of data, in anexample, each terminal device of the terminal devices (130) and (140)may code video data (e.g., a stream of video pictures that are capturedby the terminal device) for transmission to the other terminal device ofthe terminal devices (130) and (140) via the network (150). Eachterminal device of the terminal devices (130) and (140) also may receivethe coded video data transmitted by the other terminal device of theterminal devices (130) and (140), and may decode the coded video data torecover the video pictures and may display video pictures at anaccessible display device according to the recovered video data.

In the FIG. 1 example, the terminal devices (110), (120), (130) and(140) may be illustrated as servers, personal computers and smart phonesbut the principles of the present disclosure may be not so limited.Embodiments of the present disclosure find application with laptopcomputers, tablet computers, media players and/or dedicated videoconferencing equipment. The network (150) represents any number ofnetworks that convey coded video data among the terminal devices (110),(120), (130) and (140), including for example wireline (wired) and/orwireless communication networks. The communication network (150) mayexchange data in circuit-switched and/or packet-switched channels.Representative networks include telecommunications networks, local areanetworks, wide area networks and/or the Internet. For the purposes ofthe present discussion, the architecture and topology of the network(150) may be immaterial to the operation of the present disclosureunless explained herein below.

FIG. 2 illustrates, as an example for an application for the disclosedsubject matter, the placement of a video encoder and a video decoder ina streaming environment. The disclosed subject matter can be equallyapplicable to other video enabled applications, including, for example,video conferencing, digital TV, storing of compressed video on digitalmedia including CD, DVD, memory stick and the like, and so on.

A streaming system may include a capture subsystem (213), that caninclude a video source (201), for example a digital camera, creating forexample a stream of video pictures (202) that are uncompressed. In anexample, the stream of video pictures (202) includes samples that aretaken by the digital camera. The stream of video pictures (202),depicted as a bold line to emphasize a high data volume when compared toencoded video data (204) (or coded video bitstreams), can be processedby an electronic device (220) that includes a video encoder (203)coupled to the video source (201). The video encoder (203) can includehardware, software, or a combination thereof to enable or implementaspects of the disclosed subject matter as described in more detailbelow. The encoded video data (204) (or encoded video bitstream (204)),depicted as a thin line to emphasize the lower data volume when comparedto the stream of video pictures (202), can be stored on a streamingserver (205) for future use. One or more streaming client subsystems,such as client subsystems (206) and (208) in FIG. 2 can access thestreaming server (205) to retrieve copies (207) and (209) of the encodedvideo data (204). A client subsystem (206) can include a video decoder(210), for example, in an electronic device (230). The video decoder(210) decodes the incoming copy (207) of the encoded video data andcreates an outgoing stream of video pictures (211) that can be renderedon a display (212) (e.g., display screen) or other rendering device (notdepicted). In some streaming systems, the encoded video data (204),(207), and (209) (e.g., video bitstreams) can be encoded according tocertain video coding/compression standards. Examples of those standardsinclude ITU-T Recommendation H.265. In an example, a video codingstandard under development is informally known as Versatile Video Coding(VVC). The disclosed subject matter may be used in the context of VVC.

It is noted that the electronic devices (220) and (230) can includeother components (not shown). For example, the electronic device (220)can include a video decoder (not shown) and the electronic device (230)can include a video encoder (not shown) as well.

FIG. 3 shows a block diagram of a video decoder (310) according to anembodiment of the present disclosure. The video decoder (310) can beincluded in an electronic device (330). The electronic device (330) caninclude a receiver (331) (e.g., receiving circuitry). The video decoder(310) can be used in the place of the video decoder (210) in the FIG. 2example.

The receiver (331) may receive one or more coded video sequences to bedecoded by the video decoder (310); in the same or another embodiment,one coded video sequence at a time, where the decoding of each codedvideo sequence is independent from other coded video sequences. Thecoded video sequence may be received from a channel (301), which may bea hardware/software link to a storage device which stores the encodedvideo data. The receiver (331) may receive the encoded video data withother data, for example, coded audio data and/or ancillary data streams,that may be forwarded to their respective using entities (not depicted).The receiver (331) may separate the coded video sequence from the otherdata. To combat network jitter, a buffer memory (315) may be coupled inbetween the receiver (331) and an entropy decoder/parser (320) (“parser(320)” henceforth). In certain applications, the buffer memory (315) ispart of the video decoder (310). In others, it can be outside of thevideo decoder (310) (not depicted). In still others, there can be abuffer memory (not depicted) outside of the video decoder (310), forexample to combat network jitter, and in addition another buffer memory(315) inside the video decoder (310), for example to handle playouttiming. When the receiver (331) is receiving data from a store/forwarddevice of sufficient bandwidth and controllability, or from anisosynchronous network, the buffer memory (315) may not be needed, orcan be small. For use on best effort packet networks such as theInternet, the buffer memory (315) may be required, can be comparativelylarge and can be advantageously of adaptive size, and may at leastpartially be implemented in an operating system or similar elements (notdepicted) outside of the video decoder (310).

The video decoder (310) may include the parser (320) to reconstructsymbols (321) from the coded video sequence. Categories of those symbolsinclude information used to manage operation of the video decoder (310),and potentially information to control a rendering device such as arender device (312) (e.g., a display screen) that is not an integralpart of the electronic device (330) but can be coupled to the electronicdevice (330), as was shown in FIG. 3. The control information for therendering device(s) may be in the form of Supplemental EnhancementInformation (SEI messages) or Video Usability Information (VUI)parameter set fragments (not depicted). The parser (320) mayparse/entropy-decode the coded video sequence that is received. Thecoding of the coded video sequence can be in accordance with a videocoding technology or standard, and can follow various principles,including variable length coding, Huffman coding, arithmetic coding withor without context sensitivity, and so forth. The parser (320) mayextract from the coded video sequence, a set of subgroup parameters forat least one of the subgroups of pixels in the video decoder, based uponat least one parameter corresponding to the group. Subgroups can includeGroups of Pictures (GOPs), pictures, tiles, slices, macroblocks, CodingUnits (CUs), blocks, Transform Units (TUs), Prediction Units (PUs) andso forth. The parser (320) may also extract from the coded videosequence information such as transform coefficients, quantizer parametervalues, motion vectors, and so forth.

The parser (320) may perform an entropy decoding/parsing operation onthe video sequence received from the buffer memory (315), so as tocreate symbols (321).

Reconstruction of the symbols (321) can involve multiple different unitsdepending on the type of the coded video picture or parts thereof (suchas: inter and intra picture, inter and intra block), and other factors.Which units are involved, and how, can be controlled by the subgroupcontrol information that was parsed from the coded video sequence by theparser (320). The flow of such subgroup control information between theparser (320) and the multiple units below is not depicted for clarity.

Beyond the functional blocks already mentioned, the video decoder (310)can be conceptually subdivided into a number of functional units asdescribed below. In a practical implementation operating undercommercial constraints, many of these units interact closely with eachother and can, at least partly, be integrated into each other. However,for the purpose of describing the disclosed subject matter, theconceptual subdivision into the functional units below is appropriate.

A first unit is the scaler/inverse transform unit (351). Thescaler/inverse transform unit (351) receives a quantized transformcoefficient as well as control information, including which transform touse, block size, quantization factor, quantization scaling matrices,etc. as symbol(s) (321) from the parser (320). The scaler/inversetransform unit (351) can output blocks comprising sample values, thatcan be input into aggregator (355).

In some cases, the output samples of the scaler/inverse transform (351)can pertain to an intra coded block; that is: a block that is not usingpredictive information from previously reconstructed pictures, but canuse predictive information from previously reconstructed parts of thecurrent picture. Such predictive information can be provided by an intrapicture prediction unit (352). In some cases, the intra pictureprediction unit (352) generates a block of the same size and shape ofthe block under reconstruction, using surrounding already reconstructedinformation fetched from the current picture buffer (358). The currentpicture buffer (358) buffers, for example, partly reconstructed currentpicture and/or fully reconstructed current picture. The aggregator(355), in some cases, adds, on a per sample basis, the predictioninformation the intra prediction unit (352) has generated to the outputsample information as provided by the scaler/inverse transform unit(351).

In other cases, the output samples of the scaler/inverse transform unit(351) can pertain to an inter coded, and potentially motion compensatedblock. In such a case, a motion compensation prediction unit (353) canaccess reference picture memory (357) to fetch samples used forprediction. After motion compensating the fetched samples in accordancewith the symbols (321) pertaining to the block, these samples can beadded by the aggregator (355) to the output of the scaler/inversetransform unit (351) (in this case called the residual samples orresidual signal) so as to generate output sample information. Theaddresses within the reference picture memory (357) from where themotion compensation prediction unit (353) fetches prediction samples canbe controlled by motion vectors, available to the motion compensationprediction unit (353) in the form of symbols (321) that can have, forexample X, Y, and reference picture components. Motion compensation alsocan include interpolation of sample values as fetched from the referencepicture memory (357) when sub-sample exact motion vectors are in use,motion vector prediction mechanisms, and so forth.

The output samples of the aggregator (355) can be subject to variousloop filtering techniques in the loop filter unit (356). Videocompression technologies can include in-loop filter technologies thatare controlled by parameters included in the coded video sequence (alsoreferred to as coded video bitstream) and made available to the loopfilter unit (356) as symbols (321) from the parser (320), but can alsobe responsive to meta-information obtained during the decoding ofprevious (in decoding order) parts of the coded picture or coded videosequence, as well as responsive to previously reconstructed andloop-filtered sample values.

The output of the loop filter unit (356) can be a sample stream that canbe output to the render device (312) as well as stored in the referencepicture memory (357) for use in future inter-picture prediction.

Certain coded pictures, once fully reconstructed, can be used asreference pictures for future prediction. For example, once a codedpicture corresponding to a current picture is fully reconstructed andthe coded picture has been identified as a reference picture (by, forexample, the parser (320)), the current picture buffer (358) can becomea part of the reference picture memory (357), and a fresh currentpicture buffer can be reallocated before commencing the reconstructionof the following coded picture.

The video decoder (310) may perform decoding operations according to apredetermined video compression technology in a standard, such as ITU-TRec. H.265. The coded video sequence may conform to a syntax specifiedby the video compression technology or standard being used, in the sensethat the coded video sequence adheres to both the syntax of the videocompression technology or standard and the profiles as documented in thevideo compression technology or standard. Specifically, a profile canselect certain tools as the only tools available for use under thatprofile from all the tools available in the video compression technologyor standard. Also necessary for compliance can be that the complexity ofthe coded video sequence is within bounds as defined by the level of thevideo compression technology or standard. In some cases, levels restrictthe maximum picture size, maximum frame rate, maximum reconstructionsample rate (measured in, for example megasamples per second), maximumreference picture size, and so on. Limits set by levels can, in somecases, be further restricted through Hypothetical Reference Decoder(HRD) specifications and metadata for HRD buffer management signaled inthe coded video sequence.

In an embodiment, the receiver (331) may receive additional (redundant)data with the encoded video. The additional data may be included as partof the coded video sequence(s). The additional data may be used by thevideo decoder (310) to properly decode the data and/or to moreaccurately reconstruct the original video data. Additional data can bein the form of, for example, temporal, spatial, or signal noise ratio(SNR) enhancement layers, redundant slices, redundant pictures, forwarderror correction codes, and so on.

FIG. 4 shows a block diagram of a video encoder (403) according to anembodiment of the present disclosure. The video encoder (403) isincluded in an electronic device (420). The electronic device (420)includes a transmitter (440) (e.g., transmitting circuitry). The videoencoder (403) can be used in the place of the video encoder (203) in theFIG. 2 example.

The video encoder (403) may receive video samples from a video source(401) (that is not part of the electronic device (420) in the FIG. 4example) that may capture video image(s) to be coded by the videoencoder (403). In another example, the video source (401) is a part ofthe electronic device (420).

The video source (401) may provide the source video sequence to be codedby the video encoder (403) in the form of a digital video sample streamthat can be of any suitable bit depth (for example: 8 bit, 10 bit, 12bit, . . . ), any colorspace (for example, BT.601 Y CrCB, RGB, . . . ),and any suitable sampling structure (for example Y CrCb 4:2:0, Y CrCb4:4:4). In a media serving system, the video source (401) may be astorage device storing previously prepared video. In a videoconferencingsystem, the video source (401) may be a camera that captures local imageinformation as a video sequence. Video data may be provided as aplurality of individual pictures that impart motion when viewed insequence. The pictures themselves may be organized as a spatial array ofpixels, wherein each pixel can comprise one or more samples depending onthe sampling structure, color space, etc. in use. A person skilled inthe art can readily understand the relationship between pixels andsamples. The description below focuses on samples.

According to an embodiment, the video encoder (403) may code andcompress the pictures of the source video sequence into a coded videosequence (443) in real time or under any other time constraints asrequired by the application. Enforcing appropriate coding speed is onefunction of a controller (450). In some embodiments, the controller(450) controls other functional units as described below and isfunctionally coupled to the other functional units. The coupling is notdepicted for clarity. Parameters set by the controller (450) can includerate control related parameters (picture skip, quantizer, lambda valueof rate-distortion optimization techniques, . . . ), picture size, groupof pictures (GOP) layout, maximum motion vector search range, and soforth. The controller (450) can be configured to have other suitablefunctions that pertain to the video encoder (403) optimized for acertain system design.

In some embodiments, the video encoder (403) is configured to operate ina coding loop. As an oversimplified description, in an example, thecoding loop can include a source coder (430) (e.g., responsible forcreating symbols, such as a symbol stream, based on an input picture tobe coded, and a reference picture(s)), and a (local) decoder (433)embedded in the video encoder (403). The decoder (433) reconstructs thesymbols to create the sample data in a similar manner as a (remote)decoder also would create (as any compression between symbols and codedvideo bitstream is lossless in the video compression technologiesconsidered in the disclosed subject matter). The reconstructed samplestream (sample data) is input to the reference picture memory (434). Asthe decoding of a symbol stream leads to bit-exact results independentof decoder location (local or remote), the content in the referencepicture memory (434) is also bit exact between the local encoder andremote encoder. In other words, the prediction part of an encoder “sees”as reference picture samples exactly the same sample values as a decoderwould “see” when using prediction during decoding. This fundamentalprinciple of reference picture synchronicity (and resulting drift, ifsynchronicity cannot be maintained, for example because of channelerrors) is used in some related arts as well.

The operation of the “local” decoder (433) can be the same as of a“remote” decoder, such as the video decoder (310), which has alreadybeen described in detail above in conjunction with FIG. 3. Brieflyreferring also to FIG. 3, however, as symbols are available andencoding/decoding of symbols to a coded video sequence by an entropycoder (445) and the parser (320) can be lossless, the entropy decodingparts of the video decoder (310), including the buffer memory (315), andparser (320) may not be fully implemented in the local decoder (433).

An observation that can be made at this point is that any decodertechnology except the parsing/entropy decoding that is present in adecoder also necessarily needs to be present, in substantially identicalfunctional form, in a corresponding encoder. For this reason, thedisclosed subject matter focuses on decoder operation. The descriptionof encoder technologies can be abbreviated as they are the inverse ofthe comprehensively described decoder technologies. Only in certainareas a more detail description is required and provided below.

During operation, in some examples, the source coder (430) may performmotion compensated predictive coding, which codes an input picturepredictively with reference to one or more previously-coded picture fromthe video sequence that were designated as “reference pictures”. In thismanner, the coding engine (432) codes differences between pixel blocksof an input picture and pixel blocks of reference picture(s) that may beselected as prediction reference(s) to the input picture.

The local video decoder (433) may decode coded video data of picturesthat may be designated as reference pictures, based on symbols createdby the source coder (430). Operations of the coding engine (432) mayadvantageously be lossy processes. When the coded video data may bedecoded at a video decoder (not shown in FIG. 4), the reconstructedvideo sequence typically may be a replica of the source video sequencewith some errors. The local video decoder (433) replicates decodingprocesses that may be performed by the video decoder on referencepictures and may cause reconstructed reference pictures to be stored inthe reference picture cache (434). In this manner, the video encoder(403) may store copies of reconstructed reference pictures locally thathave common content as the reconstructed reference pictures that will beobtained by a far-end video decoder (absent transmission errors).

The predictor (435) may perform prediction searches for the codingengine (432). That is, for a new picture to be coded, the predictor(435) may search the reference picture memory (434) for sample data (ascandidate reference pixel blocks) or certain metadata such as referencepicture motion vectors, block shapes, and so on, that may serve as anappropriate prediction reference for the new pictures. The predictor(435) may operate on a sample block-by-pixel block basis to findappropriate prediction references. In some cases, as determined bysearch results obtained by the predictor (435), an input picture mayhave prediction references drawn from multiple reference pictures storedin the reference picture memory (434).

The controller (450) may manage coding operations of the source coder(430), including, for example, setting of parameters and subgroupparameters used for encoding the video data.

Output of all aforementioned functional units may be subjected toentropy coding in the entropy coder (445). The entropy coder (445)translates the symbols as generated by the various functional units intoa coded video sequence, by lossless compressing the symbols according totechnologies such as Huffman coding, variable length coding, arithmeticcoding, and so forth.

The transmitter (440) may buffer the coded video sequence(s) as createdby the entropy coder (445) to prepare for transmission via acommunication channel (460), which may be a hardware/software link to astorage device which would store the encoded video data. The transmitter(440) may merge coded video data from the video coder (403) with otherdata to be transmitted, for example, coded audio data and/or ancillarydata streams (sources not shown).

The controller (450) may manage operation of the video encoder (403).During coding, the controller (450) may assign to each coded picture acertain coded picture type, which may affect the coding techniques thatmay be applied to the respective picture. For example, pictures oftenmay be assigned as one of the following picture types:

An Intra Picture (I picture) may be one that may be coded and decodedwithout using any other picture in the sequence as a source ofprediction. Some video codecs allow for different types of intrapictures, including, for example Independent Decoder Refresh (“IDR”)Pictures. A person skilled in the art is aware of those variants of Ipictures and their respective applications and features.

A predictive picture (P picture) may be one that may be coded anddecoded using intra prediction or inter prediction using at most onemotion vector and reference index to predict the sample values of eachblock.

A bi-directionally predictive picture (B Picture) may be one that may becoded and decoded using intra prediction or inter prediction using atmost two motion vectors and reference indices to predict the samplevalues of each block. Similarly, multiple-predictive pictures can usemore than two reference pictures and associated metadata for thereconstruction of a single block.

Source pictures commonly may be subdivided spatially into a plurality ofsample blocks (for example, blocks of 4×4, 8×8, 4×8, or 16×16 sampleseach) and coded on a block-by-block basis. Blocks may be codedpredictively with reference to other (already coded) blocks asdetermined by the coding assignment applied to the blocks' respectivepictures. For example, blocks of I pictures may be codednon-predictively or they may be coded predictively with reference toalready coded blocks of the same picture (spatial prediction or intraprediction). Pixel blocks of P pictures may be coded predictively, viaspatial prediction or via temporal prediction with reference to onepreviously coded reference picture. Blocks of B pictures may be codedpredictively, via spatial prediction or via temporal prediction withreference to one or two previously coded reference pictures.

The video encoder (403) may perform coding operations according to apredetermined video coding technology or standard, such as ITU-T Rec.H.265. In its operation, the video encoder (403) may perform variouscompression operations, including predictive coding operations thatexploit temporal and spatial redundancies in the input video sequence.The coded video data, therefore, may conform to a syntax specified bythe video coding technology or standard being used.

In an embodiment, the transmitter (440) may transmit additional datawith the encoded video. The source coder (430) may include such data aspart of the coded video sequence. Additional data may comprisetemporal/spatial/SNR enhancement layers, other forms of redundant datasuch as redundant pictures and slices, SEI messages, VUI parameter setfragments, and so on.

A video may be captured as a plurality of source pictures (videopictures) in a temporal sequence. Intra-picture prediction (oftenabbreviated to intra prediction) makes use of spatial correlation in agiven picture, and inter-picture prediction makes uses of the (temporalor other) correlation between the pictures. In an example, a specificpicture under encoding/decoding, which is referred to as a currentpicture, is partitioned into blocks. When a block in the current pictureis similar to a reference block in a previously coded and still bufferedreference picture in the video, the block in the current picture can becoded by a vector that is referred to as a motion vector. The motionvector points to the reference block in the reference picture, and canhave a third dimension identifying the reference picture, in casemultiple reference pictures are in use.

In some embodiments, a bi-prediction technique can be used in theinter-picture prediction. According to the bi-prediction technique, tworeference pictures, such as a first reference picture and a secondreference picture that are both prior in decoding order to the currentpicture in the video (but may be in the past and future, respectively,in display order) are used. A block in the current picture can be codedby a first motion vector that points to a first reference block in thefirst reference picture, and a second motion vector that points to asecond reference block in the second reference picture. The block can bepredicted by a combination of the first reference block and the secondreference block.

Further, a merge mode technique can be used in the inter-pictureprediction to improve coding efficiency.

According to some embodiments of the disclosure, predictions, such asinter-picture predictions and intra-picture predictions are performed inthe unit of blocks. For example, according to the HEVC standard, apicture in a sequence of video pictures is partitioned into coding treeunits (CTU) for compression, the CTUs in a picture have the same size,such as 64×64 pixels, 32×32 pixels, or 16×16 pixels. In general, a CTUincludes three coding tree blocks (CTBs), which are one luma CTB and twochroma CTBs. Each CTU can be recursively quadtree split into one ormultiple coding units (CUs). For example, a CTU of 64×64 pixels can besplit into one CU of 64×64 pixels, or 4 CUs of 32×32 pixels, or 16 CUsof 16×16 pixels. In an example, each CU is analyzed to determine aprediction type for the CU, such as an inter prediction type or an intraprediction type. The CU is split into one or more prediction units (PUs)depending on the temporal and/or spatial predictability. Generally, eachPU includes a luma prediction block (PB), and two chroma PBs. In anembodiment, a prediction operation in coding (encoding/decoding) isperformed in the unit of a prediction block. Using a luma predictionblock as an example of a prediction block, the prediction block includesa matrix of values (e.g., luma values) for pixels, such as 8×8 pixels,16×16 pixels, 8×16 pixels, 16×8 pixels, and the like.

FIG. 5 shows a diagram of a video encoder (503) according to anotherembodiment of the disclosure. The video encoder (503) is configured toreceive a processing block (e.g., a prediction block) of sample valueswithin a current video picture in a sequence of video pictures, andencode the processing block into a coded picture that is part of a codedvideo sequence. In an example, the video encoder (503) is used in theplace of the video encoder (203) in the FIG. 2 example.

In an HEVC example, the video encoder (503) receives a matrix of samplevalues for a processing block, such as a prediction block of 8×8samples, and the like. The video encoder (503) determines whether theprocessing block is best coded using intra mode, inter mode, orbi-prediction mode using, for example, rate-distortion optimization.When the processing block is to be coded in intra mode, the videoencoder (503) may use an intra prediction technique to encode theprocessing block into the coded picture; and when the processing blockis to be coded in inter mode or bi-prediction mode, the video encoder(503) may use an inter prediction or bi-prediction technique,respectively, to encode the processing block into the coded picture. Incertain video coding technologies, merge mode can be an inter pictureprediction submode where the motion vector is derived from one or moremotion vector predictors without the benefit of a coded motion vectorcomponent outside the predictors. In certain other video codingtechnologies, a motion vector component applicable to the subject blockmay be present. In an example, the video encoder (503) includes othercomponents, such as a mode decision module (not shown) to determine themode of the processing blocks.

In the FIG. 5 example, the video encoder (503) includes the interencoder (530), an intra encoder (522), a residue calculator (523), aswitch (526), a residue encoder (524), a general controller (521), andan entropy encoder (525) coupled together as shown in FIG. 5.

The inter encoder (530) is configured to receive the samples of thecurrent block (e.g., a processing block), compare the block to one ormore reference blocks in reference pictures (e.g., blocks in previouspictures and later pictures), generate inter prediction information(e.g., description of redundant information according to inter encodingtechnique, motion vectors, merge mode information), and calculate interprediction results (e.g., predicted block) based on the inter predictioninformation using any suitable technique. In some examples, thereference pictures are decoded reference pictures that are decoded basedon the encoded video information.

The intra encoder (522) is configured to receive the samples of thecurrent block (e.g., a processing block), in some cases compare theblock to blocks already coded in the same picture, generate quantizedcoefficients after transform, and in some cases also intra predictioninformation (e.g., an intra prediction direction information accordingto one or more intra encoding techniques). In an example, the intraencoder (522) also calculates intra prediction results (e.g., predictedblock) based on the intra prediction information and reference blocks inthe same picture.

The general controller (521) is configured to determine general controldata and control other components of the video encoder (503) based onthe general control data. In an example, the general controller (521)determines the mode of the block, and provides a control signal to theswitch (526) based on the mode. For example, when the mode is the intramode, the general controller (521) controls the switch (526) to selectthe intra mode result for use by the residue calculator (523), andcontrols the entropy encoder (525) to select the intra predictioninformation and include the intra prediction information in thebitstream; and when the mode is the inter mode, the general controller(521) controls the switch (526) to select the inter prediction resultfor use by the residue calculator (523), and controls the entropyencoder (525) to select the inter prediction information and include theinter prediction information in the bitstream.

The residue calculator (523) is configured to calculate a difference(residue data) between the received block and prediction resultsselected from the intra encoder (522) or the inter encoder (530). Theresidue encoder (524) is configured to operate based on the residue datato encode the residue data to generate the transform coefficients. In anexample, the residue encoder (524) is configured to convert the residuedata from a spatial domain to a frequency domain, and generate thetransform coefficients. The transform coefficients are then subject toquantization processing to obtain quantized transform coefficients. Invarious embodiments, the video encoder (503) also includes a residuedecoder (528). The residue decoder (528) is configured to performinverse-transform, and generate the decoded residue data. The decodedresidue data can be suitably used by the intra encoder (522) and theinter encoder (530). For example, the inter encoder (530) can generatedecoded blocks based on the decoded residue data and inter predictioninformation, and the intra encoder (522) can generate decoded blocksbased on the decoded residue data and the intra prediction information.The decoded blocks are suitably processed to generate decoded picturesand the decoded pictures can be buffered in a memory circuit (not shown)and used as reference pictures in some examples.

The entropy encoder (525) is configured to format the bitstream toinclude the encoded block. The entropy encoder (525) is configured toinclude various information according to a suitable standard, such asthe HEVC standard. In an example, the entropy encoder (525) isconfigured to include the general control data, the selected predictioninformation (e.g., intra prediction information or inter predictioninformation), the residue information, and other suitable information inthe bitstream. Note that, according to the disclosed subject matter,when coding a block in the merge submode of either inter mode orbi-prediction mode, there is no residue information.

FIG. 6 shows a diagram of a video decoder (610) according to anotherembodiment of the disclosure. The video decoder (610) is configured toreceive coded pictures that are part of a coded video sequence, anddecode the coded pictures to generate reconstructed pictures. In anexample, the video decoder (610) is used in the place of the videodecoder (210) in the FIG. 2 example.

In the FIG. 6 example, the video decoder (610) includes an entropydecoder (671), an inter decoder (680), a residue decoder (673), areconstruction module (674), and an intra decoder (672) coupled togetheras shown in FIG. 6.

The entropy decoder (671) can be configured to reconstruct, from thecoded picture, certain symbols that represent the syntax elements ofwhich the coded picture is made up. Such symbols can include, forexample, the mode in which a block is coded (such as, for example, intramode, inter mode, bi-predicted mode, the latter two in merge submode oranother submode), prediction information (such as, for example, intraprediction information or inter prediction information) that canidentify certain sample or metadata that is used for prediction by theintra decoder (672) or the inter decoder (680), respectively, residualinformation in the form of, for example, quantized transformcoefficients, and the like. In an example, when the prediction mode isinter or bi-predicted mode, the inter prediction information is providedto the inter decoder (680); and when the prediction type is the intraprediction type, the intra prediction information is provided to theintra decoder (672). The residual information can be subject to inversequantization and is provided to the residue decoder (673).

The inter decoder (680) is configured to receive the inter predictioninformation, and generate inter prediction results based on the interprediction information.

The intra decoder (672) is configured to receive the intra predictioninformation, and generate prediction results based on the intraprediction information.

The residue decoder (673) is configured to perform inverse quantizationto extract de-quantized transform coefficients, and process thede-quantized transform coefficients to convert the residual from thefrequency domain to the spatial domain. The residue decoder (673) mayalso require certain control information (to include the QuantizerParameter (QP)), and that information may be provided by the entropydecoder (671) (data path not depicted as this may be low volume controlinformation only).

The reconstruction module (674) is configured to combine, in the spatialdomain, the residual as output by the residue decoder (673) and theprediction results (as output by the inter or intra prediction modulesas the case may be) to form a reconstructed block, that may be part ofthe reconstructed picture, which in turn may be part of thereconstructed video. It is noted that other suitable operations, such asa deblocking operation and the like, can be performed to improve thevisual quality.

It is noted that the video encoders (203), (403), and (503), and thevideo decoders (210), (310), and (610) can be implemented using anysuitable technique. In an embodiment, the video encoders (203), (403),and (503), and the video decoders (210), (310), and (610) can beimplemented using one or more integrated circuits. In anotherembodiment, the video encoders (203), (403), and (403), and the videodecoders (210), (310), and (610) can be implemented using one or moreprocessors that execute software instructions.

Aspects of the disclosure provide techniques for the next-generationvideo coding beyond HEVC (High Efficiency Video Coding), e.g., VersatileVideo Coding (VVC). More specifically, a scheme for predicting the DCvalues applied in sub transform units is disclosed.

ITU-T VCEG (Q6/16) and ISO/IEC MPEG (JTC 1/SC 29/WG 11) published theH.265/HEVC (High Efficiency Video Coding) standard in 2013 (version 1),2014 (version 2), 2015 (version 3) and 2016 (version 4). Since then theITU-T and ISO/IEC have been studying the potential need forstandardization of future video coding technology with a compressioncapability that significantly exceeds that of the HEVC standard(including its extensions). In October 2017, the ITU-T and ISO/IECissued the Joint Call for Proposals on Video Compression with Capabilitybeyond HEVC (CfP). By Feb. 15, 2018, total 22 CfP responses on standarddynamic range (SDR), 12 CfP responses on high dynamic range (HDR), and12 CfP responses on 360 video categories were submitted, respectively.In April 2018, all received CfP responses were evaluated in the 122MPEG/10th JVET (Joint Video Exploration Team—Joint Video Expert Team)meeting. With careful evaluation, JVET formally launched thestandardization of next-generation video coding beyond HEVC, i.e., theso-called Versatile Video Coding (VVC).

In HEVC, a coding tree unit (CTU) can be split into a plurality ofcoding units (CUs) by using a quadtree structure that is denoted as acoding tree to adapt to various local characteristics. A decision onwhether to code a picture area using inter-picture (temporal) orintra-picture (spatial) prediction is made at the CU level. Each CU canbe further split into one, two or four prediction units (PUs) accordingto the PU splitting type. Inside one PU, the same prediction process isapplied and the relevant information is transmitted to the decoder on aPU basis. After obtaining the residual block by applying the predictionprocess based on the PU splitting type, a CU can be partitioned intotransform units (TUs) according to another quadtree structure like thecoding tree for the CU. One of key features of the HEVC structure isthat the HEVC has the multiple partition conceptions including CU, PU,and TU. In HEVC, a CU or a TU can only be square shape, while a PU maybe square or rectangular shape for an inter predicted block. In HEVC,one coding block may be further split into four square sub-blocks, andtransform is performed on each sub-block, i.e., TU. Each TU can befurther split recursively (using quadtree split) into smaller TUs, whichis called Residual Quad-Tree (RQT).

At a picture boundary, HEVC employs implicit quad-tree split so that ablock will keep quad-tree splitting until the size fits the pictureboundary.

As mentioned above, in HEVC, a CTU is split into a plurality of CUs byusing a quadtree structure that is denoted as a coding tree to adapt tovarious local characteristics. The decision on whether to code a picturearea using inter-picture (temporal) or intra-picture (spatial)prediction is made at the CU level. Each CU can be further split intoone, two or four PUs according to the PU splitting type. Inside one PU,the same prediction process is applied and the relevant information istransmitted to the decoder on a PU basis. After obtaining the residualblock by applying the prediction process based on the PU splitting type,a CU can be partitioned into transform units (TUs) according to anotherquadtree structure like the coding tree for the CU. One of key featuresof the HEVC structure is that it has the multiple partition conceptionsincluding CU, PU, and TU.

In VVC, a block partitioning structure using quad-tree (QT) plus binarytree (BT) is proposed. The QTBT structure removes the concepts ofmultiple partition types, i.e., the QTBT structure removes theseparation of the CU, PU and TU concepts, and supports more flexibilityfor CU partition shapes. In the QTBT block structure (or QTBTstructure), a CU can have either a square or rectangular shape. As shownin FIGS. 7A and 7B, a coding tree unit (CTU) is first partitioned by aquadtree structure. The quadtree leaf nodes are further partitioned by abinary tree structure. There are two splitting types, symmetrichorizontal splitting and symmetric vertical splitting, in the binarytree splitting. The binary tree leaf nodes are called coding units(CUs), and that segmentation is used for prediction and transformprocessing without any further partitioning. This means that the CU, PUand TU have the same block size in the QTBT coding block structure. Inthe experimental software Jiont Exploration Model (JEM), a CU sometimesconsists of coding blocks (CBs) of different colour components, e.g.,one CU contains one luma CB and two chroma CBs in the case of P and Bslices of the 4:2:0 chroma format and sometimes consists of a CB of asingle component, e.g., one CU contains only one luma CB or just twochroma CBs in the case of I slices.

In some embodiments, following parameters are defined for the QTBTpartitioning scheme: (1) CTU size refers to a root node size of aquadtree, which has a same concept as in HEVC; (2) MinQTSize refers to aminimum allowed quadtree leaf node size; (3) MaxBTSize refers to amaximum allowed binary tree root node size; (4) MaxBTDepth refers to amaximum allowed binary tree depth; and (5) MinBTSize refers to a minimumallowed binary tree leaf node size.

In one example of the QTBT partitioning structure (or QTBT structure),the CTU size is set as 128×128 luma samples with two corresponding 64×64blocks of chroma samples, the MinQTSize is set as 16×16, the MaxBTSizeis set as 64×64, the MinBTSize (for both width and height) is set as4×4, and the MaxBTDepth is set as 4. The quadtree partitioning isapplied to the CTU first to generate a plurality of quadtree leaf nodes.The quadtree leaf nodes may have a size from 16×16 (i.e., the MinQTSize)to 128×128 (i.e., the CTU size). If the leaf quadtree node is 128×128,the leaf quadtree will not be further split by the binary tree since thesize exceeds the MaxBTSize (i.e., 64×64). Otherwise, the leaf quadtreenode could be further partitioned by the binary tree. Therefore, thequadtree leaf node is also the root node for the binary tree and thequadtree leaf has the binary tree depth as 0. When the binary tree depthreaches MaxBTDepth (i.e., 4), no further splitting is considered. Whenthe binary tree node has a width equal to MinBTSize (i.e., 4), nofurther horizontal splitting is considered. Similarly, when the binarytree node has a height equal to MinBTSize, no further vertical splittingis considered. The leaf nodes of the binary tree are further processedby prediction and transform processing without any further partitioning.In the JEM, the maximum CTU size can be 256×256 luma samples.

FIG. 7A illustrates an example of block partitioning by using QTBT, andFIG. 7B illustrates the corresponding tree representation. The solidlines indicate quadtree splitting and dotted lines indicate binary treesplitting. In each splitting (i.e., non-leaf) node of the binary tree,one flag is signalled to indicate which splitting type (i.e., horizontalor vertical) is used, where 0 indicates horizontal splitting and 1indicates vertical splitting. For the quadtree splitting, there is noneed to indicate the splitting type since quadtree splitting alwayssplits a block both horizontally and vertically to produce 4 sub-blockswith an equal size.

In addition, the QTBT scheme (or QTBT structure) supports theflexibility for the luma and chroma to have a separate QTBT structure.Currently, for P and B slices, the luma and chroma CTBs in one CTU sharethe same QTBT structure. However, for I slices, the luma CTB ispartitioned into CUs by a QTBT structure, and the chroma CTBs arepartitioned into chroma CUs by another QTBT structure. This means that aCU in an I slice consists of a coding block of the luma component orcoding blocks of two chroma components, and a CU in a P or B sliceconsists of coding blocks of all three colour components.

In HEVC, inter prediction for small blocks is restricted to reduce thememory access of motion compensation, such that bi-prediction is notsupported for 4×8 and 8×4 blocks, and inter prediction is not supportedfor 4×4 blocks. In the QTBT as implemented in the JEM-7.0, theserestrictions are removed.

In VCC, a Multi-type-tree (MTT) structure is also proposed. The MTT is amore flexible tree structure than QTBT. In MTT, other than quad-tree andbinary-tree, horizontal and vertical center-side triple-trees areintroduced, as shown in FIGS. 8A and 8B. FIG. 8A is a verticalcenter-side triple-tree partitioning, and FIG. 8B is a horizontalcenter-side triple-tree partitioning. The key benefits of thetriple-tree partitioning are: (a) the triple-tree partitioning iscomplement to quad-tree and binary-tree partitioning. The triple-treepartitioning is able to capture objects which locate in block centerwhile quad-tree and binary-tree are always splitting along block center.(b) The width and height of the partitions of the proposed triple treesare always power of 2 so that no additional transforms are needed. Thedesign of two-level tree is mainly motivated by complexity reduction.Theoretically, the complexity of traversing of a tree is T^(D), where Tdenotes the number of split types, and D is the depth of tree.

In HEVC, the primary transforms are 4-point, 8-point, 16-point and32-point DCT-2, and the transform core matrices are represented using8-bit integers, i.e., 8-bit transform core. The transform core matricesof smaller DCT-2 are part of larger DCT-2, as shown below.

4 × 4 transform {64, 64, 64, 64} {83, 36, −36, −83} {64, −64, −64, 64}{36, −83, 83, −36} 8 × 8 transform {64, 64, 64, 64, 64, 64, 64, 64} {89,75, 50, 18, −18, −50, −75, −89} {83, 36, −36, −83, −83, −36, 36, 83}{75, −18, −89, −50, 50, 89, 18, −75} {64, −64, −64, 64, 64, −64, −64,64} {50, −89, 18, 75, −75, −18, 89, −50} {36, −83, 83, −36, −36, 83,−83, 36} {18, −50, 75, −89, 89, −75, 50, −18} 16 × 16 transform {64 6464 64 64 64 64 64 64 64 64 64 64 64 64 64} {90 87 80 70 57 43 25 9 −9−25 −43 −57 −70 −80 −87 −90} {89 75 50 18 −18 −50 −75 −89 −89 −75 −50−18 18 50 75 89} {87 57 9 −43 −80 −90 −70 −25 25 70 90 80 43 −9 −57 −87}{83 36 −36 −83 −83 −36 36 83 83 36 −36 −83 −83 −36 36 83} {80 9 −70 −87−25 57 90 43 −43 −90 −57 25 87 70 −9 −80} {75 −18 −89 −50 50 89 18 −75−75 18 89 50 −50 −89 −18 75} {70 −43 −87 9 90 25 −80 −57 57 80 −25 −90−9 87 43 −70} {64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 64 −64 −64 64}{57 −80 −25 90 −9 −87 43 70 −70 −43 87 9 −90 25 80 −57} {50 −89 18 75−75 −18 89 −50 −50 89 −18 −75 75 18 −89 50} {43 −90 57 25 −87 70 9 −8080 −9 −70 87 −25 −57 90 −43} {36 −83 83 −36 −36 83 −83 36 36 −83 83 −36−36 83 −83 36} {25 −70 90 −80 43 9 −57 87 −87 57 −9 −43 80 −90 70 −25}{18 −50 75 −89 89 −75 50 −18 −18 50 −75 89 −89 75 −50 18} {9 −25 43 −5770 −80 87 −90 90 −87 80 −70 57 −43 25 −9} 32 × 32 transform {64 64 64 6464 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 6464 64 64 64} {90 90 88 85 82 78 73 67 61 54 46 38 31 22 13 4 −4 −13 −22−31 −38 −46 −54 −61 −67 −73 −78 −82 −85 −88 −90 −90} {90 87 80 70 57 4325 9 −9 −25 −43 −57 −70 −80 −87 −90 −90 −87 −80 −70 −57 −43 −25 −9 9 2543 57 70 80 87 90} {90 82 67 46 22 −4 −31 −54 −73 −85 −90 −88 −78 −61−38 −13 13 38 61 78 88 90 85 73 54 31 4 −22 −46 −67 −82 −90} {89 75 5018 −18 −50 −75 −89 −89 −75 −50 −18 18 50 75 89 89 75 50 18 −18 −50 −75−89 −89 −75 −50 −18 18 50 75 89} {88 67 31 −13 −54 −82 −90 −78 −46 −4 3873 90 85 61 22 −22 −61 −85 −90 −73 −38 4 46 78 90 82 54 13 −31 −67 −88}{87 57 9 −43 −80 −90 −70 −25 25 70 90 80 43 −9 −57 −87 −87 −57 −9 43 8090 70 25 −25 −70 −90 −80 −43 9 57 87} {85 46 −13 −67 −90 −73 −22 38 8288 54 −4 −61 −90 −78 −31 31 78 90 61 4 −54 −88 −82 −38 22 73 90 67 13−46 −85} {83 36 −36 −83 −83 −36 36 83 83 36 −36 −83 −83 −36 36 83 83 36−36 −83 −83 −36 36 83 83 36 −36 −83 −83 −36 36 83} {82 22 −54 −90 −61 1378 85 31 −46 −90 −67 4 73 88 38 −38 −88 −73 −4 67 90 46 −31 −85 −78 −1361 90 54 −22 −82} {80 9 −70 −87 −25 57 90 43 −43 −90 −57 25 87 70 −9 −80−80 −9 70 87 25 −57 −90 −43 43 90 57 −25 −87 −70 9 80} {78 −4 −82 −73 1385 67 −22 −88 −61 31 90 54 −38 −90 −46 46 90 38 −54 −90 −31 61 88 22 −67−85 −13 73 82 4 −78} {75 −18 −89 −50 50 89 18 −75 −75 18 89 50 −50 −89−18 75 75 −18 −89 −50 50 89 18 −75 −75 18 89 50 −50 −89 −18 75} {73 −31−90 −22 78 67 −38 −90 −13 82 61 −46 −88 −4 85 54 −54 −85 4 88 46 −61 −8213 90 38 −67 −78 22 90 31 −73} {70 −43 −87 9 90 25 −80 −57 57 80 −25 −90−9 87 43 −70 −70 43 87 −9 −90 −25 80 57 −57 −80 25 90 9 −87 −43 70} {67−54 −78 38 85 −22 −90 4 90 13 −88 −31 82 46 −73 −61 61 73 −46 −82 31 88−13 −90 −4 90 22 −85 −38 78 54 −67} {64 −64 −64 64 64 −64 −64 64 64 −64−64 64 64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 64 −64 −64 64 64 −64−64 64} {61 −73 −46 82 31 −88 −13 90 −4 −90 22 85 −38 −78 54 67 −67 −5478 38 −85 −22 90 4 −90 13 88 −31 −82 46 73 −61} {57 −80 −25 90 −9 −87 4370 −70 −43 87 9 −90 25 80 −57 −57 80 25 −90 9 87 −43 −70 70 43 −87 −9 90−25 −80 57} {54 −85 −4 88 −46 −61 82 13 −90 38 67 −78 −22 90 −31 −73 7331 −90 22 78 −67 −38 90 −13 −82 61 46 −88 4 85 −54} {50 −89 18 75 −75−18 89 −50 −50 89 −18 −75 75 18 −89 50 50 −89 18 75 −75 −18 89 −50 −5089 −18 −75 75 18 −89 50} {46 −90 38 54 −90 31 61 −88 22 67 −85 13 73 −824 78 −78 −4 82 −73 −13 85 −67 −22 88 −61 −31 90 −54 −38 90 −46} {43 −9057 25 −87 70 9 −80 80 −9 −70 87 −25 −57 90 −43 −43 90 −57 −25 87 −70 −980 −80 9 70 −87 25 57 −90 43} { 38 −88 73 −4 −67 90 −46 −31 85 −78 13 61−90 54 22 −82 82 −22 −54 90 −61 −13 78 −85 31 46 −90 67 4 −73 88 −38}{36 −83 83 −36 −36 83 −83 36 36 −83 83 −36 −36 83 −83 36 36 −83 83 −36−36 83 −83 36 36 −83 83 −36 −36 83 −83 36} {31 −78 90 −61 4 54 −88 82−38 −22 73 −90 67 −13 −46 85 −85 46 13 −67 90 −73 22 38 −82 88 −54 −4 61−90 78 −31} {25 −70 90 −80 43 9 −57 87 −87 57 −9 −43 80 −90 70 −25 −2570 −90 80 −43 −9 57 −87 87 −57 9 43 −80 90 −70 25} {22 −61 85 −90 73 −38−4 46 −78 90 −82 54 −13 −31 67 −88 88 −67 31 13 −54 82 −90 78 −46 4 38−73 90 −85 61 −22} {18 −50 75 −89 89 −75 50 −18 −18 50 −75 89 −89 75 −5018 18 −50 75 −89 89 −75 50 −18 −18 50 −75 89 −89 75 −50 18} {13 −38 61−78 88 −90 85 −73 54 −31 4 22 −46 67 −82 90 −90 82 −67 46 −22 −4 31 −5473 −85 90 −88 78 −61 38 −13} { 9 −25 43 −57 70 −80 87 −90 90 −87 80 −7057 −43 25 −9 −9 25 −43 57 −70 80 −87 90 −90 87 −80 70 −57 43 −25 9} { 4−13 22 −31 38 −46 54 −61 67 −73 78 −82 85 −88 90 −90 90 −90 88 −85 82−78 73 −67 61 −54 46 −38 31 −22 13 −4}

The DCT-2 cores show symmetry/anti-symmetry characteristics. Thus, aso-called “partial butterfly” implementation is supported to reduce thenumber of operation counts (multiplications, adds/subs, shifts), andidentical results of matrix multiplication can be obtained using partialbutterfly.

In current VVC, besides 4-point, 8-point, 16-point and 32-point DCT-2transforms which are same with HEVC, additional 2-point and 64-pointDCT-2 are also included. The 64-point DCT-2 core defined in VVC is shownbelow as a 64×64 matrix:

{ { aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, { aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa,aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa, aa ) { bf, bg, bh, bi, bj,bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb,cc, cd, ce, cf, cg, ch, ci, cj, ck, -ck, -cj, -ci, -ch, -cg, -cf, -ce,-cd, -cc, -cb, -ca, -bz, -by, -bx, -bw, -bv, -bu, -bt, -bs, -br, -bg,-bp, -bo, -bn, -bm, -bl, -bk, -bj, -bi, -bh, -bg, -bf } { ap, aq, ar,as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, -be, -bd, -bc, -bb,-ba, -az, -ay, -ax, -aw, -av, -au, -at, -as, -ar, -aq, -ap, -ap, -aq,-ar, -as, -at, -au, -av, -aw, -ax, -ay, -az, -ba, -bb, -bc, -bd, -be,-be, bd, bc, bb, ba, az, ay, ax, aw, av, au, at, as, ar, aq, ap } { bg,bj, bm, bp, bs, bv, by, cb, ce, ch, ck, -ci, -cf, -cc, -bz, -bw, -bt,-bq, -bn, -bk, -bh, -bf, -bi, -bl, -bo, -br, -bu, -bx, -ca, -cd, -cg,-cj, cj, cg, cd, ca, bx, bu, br, bo, bl, bi, bf, bh, bk, bn, bq, bt, bw,bz, cc, cf, ci, -ck, -ch, -ce, -cb, -by, -bv, -bs, -bp, -bm, -bj, -bg }{ ah, ai, aj, ak, al, am, an, ao, -ao, -an, -am, -al, -ak, -aj, -ai,-ah, -ah, -ai, -aj, -ak, -al, -am, -an, -ao, ao, an, am, al, ak, aj, ai,ah, ah, ai, aj, ak, al, am, an, ao, -ao, -an, -am, -al, -ak, -aj, -ai,-ah, -ah, -ai, -aj, -ak, -al, -am, -an, -ao, ao, an, am, al, ak, aj, ai,ah } { bh, bm, br, bw, cb, cg, -ck, -cf, -ca, -bv, -bq, -bl, -bg, -bi,-bn, -bs, -bx, -cc, -ch, cj, ce, bz, bu, bp, bk, bf, bj, bo, bt, by, cd,ci, -ci, -cd, -by, -bt, -bo, -bj, -bf, -bk, -bp, -bu, -bz, -ce, -cj, ch,cc, bx, bs, bn, bi, bg, bl, bq, bv, ca, cf, ck, -cg, -cb, -bw, -br, -bm,-bh } { aq, at, aw, az, bc, -be, -bb, -ay, -av, -as, -ap, -ar, -au, -ax,-ba, -bd, bd, ba, ax, au, ar, ap, as, av, ay, bb, be, -bc, -az, -aw,-at, -aq, -aq, -at, -aw, -az, -bc, be, bb, ay, av, as, ap, ar, au, ax,ba, bd, -bd, -ba, -ax, -au, -ar, -ap, -as, -av, -ay, -bb, -be, bc, az,aw, at, aq } { bi, bp, bw, cd, ck, -ce, -bx, -bq, -bj, -bh, -bo, -bv,-cc, -cj, cf, by, br, bk, bg, bn, bu, cb, ci, -cg, -bz, -bs, -bl, -bf,-bm, -bt, -ca, -ch, ch, ca, bt, bm, bf, bl, bs, bz, cg, -ci, -cb, -bu,-bn, -bg, -bk, -br, -by, -cf, cj, cc, bv, bo, bh, bj, bq, bx, ce, -ck,-cd, -bw, -bp, -bi } { ad, ae, af, ag, -ag, -af, -ae, -ad, -ad, -ae,-af, -ag, ag, af, ae, ad, ad, ae, af, ag, -ag, -af, -ae, -ad, -ad, -ae,-af, -ag, ag, af, ae, ad, ad, ae, af, ag, -ag, -af, -ae, -ad, -ad, -ae,-af, -ag, ag, af, ae, ad, ad, ae, af, ag, -ag, -af, -ae, -ad, -ad, -ae,-af, -ag, ag, af, ae, ad } { bj, bs, cb, ck, -cc, -bt, -bk, -bi, -br,-ca, -cj, cd, bu, bl, bh, bq, bz, ci, -ce, -bv, -bm, -bg, -bp, -by, -ch,cf, bw, bn, bf, bo, bx, cg, -cg, -bx, -bo, -bf, -bn, -bw, -cf, ch, by,bp, bg, bm, bv, ce, -ci, -bz, -bg, -bh, -bi, -bu, -cd, cj, ca, br, bi,bk, bt, cc, -ck, -cb, -bs, -bj } { ar, aw, bb, -bd, -ay, -at, -ap, -au,-az, -be, ba, av, aq, as, ax, bc, -bc, -ax, -as, -aq, -av, -ba, be, az,au, ap, at, ay, bd, -bb, -aw, -ar, -ar, -aw, -bb, bd, ay, at, ap, au,az, be, -ba, -av, -aq, -as, -ax, -bc, bc, ax, as, aq, av, ba, -be, -az,-au, -ap, -at, -ay, -bd, bb, aw, ar } { bk, bv, cg, -ce, -bt, -bi, -bm,-bx, -ci, cc, br, bg, bo, bz, ck, -ca, -bp, -bf, -bq, -cb, cj, by, bn,bh, bs, cd, -ch, -bw, -bl, -bj, -bu, -cf, cf, bu, bj, bl, bw, ch, -cd,-bs, -bh, -bn, -by, -cj, cb, bq, bf, bp, ca, -ck, -bz, -bo, -bg, -br,-cc, ci, bx, bm, bi, bt, ce, -cg, -bv, -bk } { ai, al, ao, -am, -aj,-ah, -ak, -an, an, ak, ah, aj, am, -ao, -al, -ai, -ai, -al, -ao, am, aj,ah, ak, an, -an, -ak, -ah, -aj, -am, ao, al, ai, ai, al, ao, -am, -aj,-ah, -ak, -an, an, ak, ah, aj, am, -ao, -al, -ai, -ai, -al, -ao, am, aj,ah, ak, an, -an, -ak, -ah, -aj, -am, ao, al, ai } { bl, by, -ck, -bx,-bk, -bm, -bz, cj, bw, bj, bn, ca, -ci, -bv, -bi, -bo, -cb, ch, bu, bh,bp, cc, -cg, -bt, -bg, -bq, -cd, cf, bs, bf, br, ce, -ce, -br, -bf, -bs,-cf, cd, bq, bg, bt, cg, -cc, -bp, -bh, -bu, -ch, cb, bo, bi, bv, ci,-ca, -bn, -bj, -bw, -cj, bz, bm, bk, bx, ck, -by, -bl } { as, az, -bd,-aw, -ap, -av, -bc, ba, at, ar, ay, -be, -ax, -aq, -au, -bb, bb, au, aq,ax, be, -ay, -ar, -at, -ba, bc, av, ap, aw, bd, -az, -as, -as, -az, bd,aw, ap, av, bc, -ba, -at, -ar, -ay, be, ax, aq, au, bb, -bb, -au, -aq,-ax, -be, ay, ar, at, ba, -bc, -av, -ap, -aw, -bd, az, as } { bm, cb,-cf, -bq, -bi, -bx, cj, bu, bf, bt, ci, -by, -bj, -bp, -ce, cc, bn, bl,ca, -cg, -br, -bh, -bw, ck, bv, bg, bs, ch, -bz, -bk, -bo, -cd, cd, bo,bk, bz, -ch, -bs, -bg, -bv, -ck, bw, bh, br, cg, -ca, -bl, -bn, -cc, ce,bp, bj, by, -ci, -bt, -bf, -bu, -cj, bx, bi, bq, cf, -cb, -bm } { ab,ac, -ac, -ab, -ab, -ac, ac, ab, ab, ac, -ac, -ab, -ab, -ac, ac, ab, ab,ac, -ac, -ab, -ab, -ac, ac, ab, ab, ac, -ac, -ab, -ab, -ac, ac, ab, ab,ac, -ac, -ab, -ab, -ac, ac, ab, ab, ac, -ac, -ab, -ab, -ac, ac, ab, ab,ac, -ac, -ab, -ab, -ac, ac, ab, ab, ac, -ac, -ab, -ab, -ac, ac, ab } {bn, ce, -ca, -bj, -br, -ci, bw, bf, bv, -cj, -bs, -bi, -bz, cf, bo, bm,cd, -cb, -bk, -bq, -ch, bx, bg, bu, -ck, -bt, -bh, -by, cg, bp, bl, cc,-cc, -bl, -bp, -cg, by, bh, bt, ck, -bu, -bg, -bx, ch, bq, bk, cb, -cd,-bm, -bo, -cf, bz, bi, bs, cj, -bv, -bf, -bw, ci, br, bj, ca, -ce, -bn }{ at, bc, -ay, -ap, -ax, bd, au, as, bb, -az, -aq, -aw, be, av, ar, ba,-ba, -ar, -av, -be, aw, aq, az, -bb, -as, -au, -bd, ax, ap, ay, -bc,-at, -at, -bc, ay, ap, ax, -bd, -au, -as, -bb, az, aq, aw, -be, -av,-ar, -ba, ba, ar, av, be, -aw, -aq, -az, bb, as, au, bd, -ax, -ap, -ay,bc, at } { bo, ch, -bv, -bh, -ca, cc, bj, bt, -cj, -bq, -bm, -cf, bx,bf, by, -ce, -bl, -br, -ck, bs, bk, cd, -bz, -bg, -bw, cg, bn, bp, ci,-bu, -bi, -cb, cb, bi, bu, -ci, -bp, -bn, -cg, bw, bg, bz, -cd, -bk,-bs, ck, br, bl, ce, -by, -bf, -bx, cf, bm, bq, cj, -bt, -bj, -cc, ca,bh, bv, -ch, -bo } { aj, ao, -ak, -ai, -an, al, ah, am, -am, -ah, -al,an, ai, ak, -ao, -aj, -aj, -ao, ak, ai, an, -al, -ah, -am, am, ah, al,-an, -ai, -ak, ao, aj, aj, ao, -ak, -ai, -an, al, ah, am, -am, -ah, -al,an, ai, ak, -ao, -aj, -aj, -ao, ak, ai, an, -al, -ah, -am, am, ah, al,-an, -ai, -ak, ao, aj } { bp, ck, -bq, -bo, -cj, br, bn, ci, -bs, -bm,-ch, bt, bl, cg, -bu, -bk, -cf, bv, bj, ce, -bw, -bi, -cd, bx, bh, cc,-by, -bg, -cb, bz, bf, ca, -ca, -bf, -bz, cb, bg, by, -cc, -bh, -bx, cd,bi, bw, -ce, -bj, -bv, cf, bk, bu, -cg, -bl, -bt, ch, bm, bs, -ci, -bn,-br, cj, bo, bq, -ck, -bp } { au, -be, -at, -av, bd, as, aw, -bc, -ar,-ax, bb, aq, ay, -ba, -ap, -az, az, ap, ba, -ay, -aq, -bb, ax, ar, bc,-aw, -as, -bd, av, at, be, -au, -au, be, at, av, -bd, -as, -aw, bc, ar,ax, -bb, -aq, -ay, ba, ap, az, -az, -ap, -ba, ay, aq, bb, -ax, -ar, -bc,aw, as, bd, -av, -at, -be, au } { bq, -ci, -bl, -bv, cd, bg, ca, -by,-bi, -cf, bt, bn, ck, -bo, -bs, cg, bj, bx, -cb, -bf, -cc, bw, bk, ch,-br, -bp, cj, bm, bu, -ce, -bh, -bz, bz, bh, ce, -bu, -bm, -cj, bp, br,-ch, -bk, -bw, cc, bf, cb, -bx, -bj, -cg, bs, bo, -ck, -bn, -bt, cf, bi,by, -ca, -bg, -cd, bv, bl, ci, -bq } { ae, -ag, -ad, -af, af, ad, ag,-ae, -ae, ag, ad, af, -af, -ad, -ag, ae, ae, -ag, -ad, -af, af, ad, ag,-ae, -ae, ag, ad, af, -af, -ad, -ag, ae, ae, -ag, -ad, -af, af, ad, ag,-ae, -ae, ag, ad, af, -af, -ad, -ag, ae, ae, -ag, -ad, -af, af, ad, ag,-ae, -ae, ag, ad, af, -af, -ad, -ag, ae } { br, -cf, -bg, -cc, bu, bo,-ci, -bj, -bz, bx, bl, ck, -bm, -bw, ca, bi, ch, -bp, -bt, cd, bf, ce,-bs, -bq, cg, bh, cb, -bv, -bn, cj, bk, by, -by, -bk, -cj, bn, bv, -cb,-bh, -cg, bq, ba, -ce, -bf, -cd, bt, bp, -ch, -bi, -ca, bw, bm, -ck,-bl, -bx, bz, bj, ci, -bo, -bu, cc, bg, cf, -br } { av, -bb, -ap, -bc,au, aw, -ba, -aq, -bd, at, ax, -az, -ar, -be, as, ay, -ay, -as, be, ar,az, -ax, -at, bd, aq, ba, -aw, -au, bc, ap, bb, -av, -av, bb, ap, bc,-au, -aw, ba, aq, bd, -at, -ax, az, ar, be, -as, -ay, ay, as, -be, -ar,-az, ax, at, -bd, -ag, -ba, aw, au, -bc, -ap, -bb, av } { bs, -cc, -bi,-cj, bl, bz, -bv, -bp, cf, bf, cg, -bo, -bw, by, bm, -ci, -bh, -cd, br,bt, -cb, -bj, -ck, bk, ca, -bu, -bq, ce, bg, ch, -bn, -bx, bx, bn, -ch,-bg, -ce, bq, bu, -ca, -bk, ck, bj, cb, -bt, -br, cd, bh, ci, -bm, -by,bw, bo, -cg, -bf, -cf, bp, bv, -bz, -bl, cj, bi, cc, -bs } { ak, -am,-ai, ao, ah, an, -aj, -al, al, aj, -an, -ah, -ao, ai, am, -ak, -ak, am,ai, -ao, -ah, -an, aj, al, -al, -aj, an, ah, ao, -ai, -am, ak, ak, -am,-ai, ao, ah, an, -aj, -al, al, aj, -an, -ah, -ao, ai, am, -ak, -ak, am,ai, -ao, -ah, -an, aj, al, -al, -aj, an, ah, ao, -ai, -am, ak } { bt,-bz, -bn, cf, bh, ck, -bi, -ce, bo, by, -bu, -bs, ca, bm, -cg, -bg, -cj,bj, cd, -bp, -bx, bv, br, -cb, -bl, ch, bf, ci, -bk, -cc, bq, bw, -bw,-bq, cc, bk, -ci, -bf, -ch, bl, cb, -br, -bv, bx, bp, -cd, -bj, cj, bg,cg, -bm, -ca, bs, bu, -by, -bo, ce, bi, -ck, -bh, -cf, bn, bz, -bt } {aw, -ay, -au, ba, as, -bc, -aq, be, ap, bd, -ar, -bb, at, az, -av, -ax,ax, av, -az, -at, bb, ar, -bd, -ap, -be, aq, bc, -as, -ba, au, ay, -aw,-aw, ay, au, -ba, -as, bc, aq, -be, -ap, -bd, ar, bb, -at, -az, av, ax,-ax, -av, az, at, -bb, -ar, bd, ap, be, -aq, -bc, as, ba, -au, -ay, aw }{ bu, -bw, -bs, by, bq, -ca, -bo, cc, bm, -ce, -bk, cg, bi, -ci, -bg,ck, bf, cj, -bh, -ch, bj, cf, -bl, -cd, bn, cb, -bp, -bz, br, bx, -bt,-bv, bv, bt, -bx, -br, bz, bp, -cb, -bn, cd, bl, -cf, -bj, ch, bh, -cj,-bf, -ck, bg, ci, -bi, -cg, bk, ce, -bm, -cc, bo, ca, -bq, -by, bs, bw,-bu } { aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,-aa, aa } { bv, -bt, -bx, br, bz, -bp, -cb, bn, cd, -bl, -cf, bj, ch,-bh, -cj, bf, -ck, -bg, ci, bi, -cg, -bk, ce, bm, -cc, -bo, ca, bg, -by,-bs, bw, bu, -bu, -bw, bs, by, -bq, -ca, bo, cc, -bm, -ce, bk, cg, -bi,-ci, bg, ck, -bf, cj, bh, -ch, -bj, cf, bl, -cd, -bn, cb, bp, -bz, -br,bx, bt, -bv } { ax, -av, -az, at, bb, -ar, -bd, ap, -be, -aq, bc, as,-ba, -au, ay, aw, -aw, -ay, au, ba, -as, -bc, aq, be, -ap, bd, ar, -bb,-at, az, av, -ax, -ax, av, az, -at, -bb, ar, bd, -ap, be, aq, -bc, -as,ba, au, -ay, -aw, aw, ay, -au, -ba, as, bc, -aq, -be, ap, -bd, -ar, bb,at, -az, -av, ax } { bw, -bq, -cc, bk, ci, -bf, ch, bl, -cb, -br, bv,bx, -bp, -cd, bj, cj, -bg, cg, bm, -ca, -bs, bu, by, -bo, -ce, bi, ck,-bh, cf, bn, -bz, -bt, bt, bz, -bn, -cf, bh, -ck, -bi, ce, bo, -by, -bu,bs, ca, -bm, -cg, bg, -cj, -bj, cd, bp, -bx, -bv, br, cb, -bl, -ch, bf,-ci, -bk, cc, bq, -bw } { al, -aj, -an, ah, -ao, -ai, am, ak, -ak, -am,ai, ao, -ah, an, aj, -al, -al, aj, an, -ah, ao, ai, -am, -ak, ak, am,-ai, -ao, ah, -an, -aj, al, al, -aj, -an, ah, -ao, -ai, am, ak, -ak,-am, ai, ao, -ah, an, aj, -al, -al, aj, an, -ah, ao, ai, -am, -ak, ak,am, -ai, -ao, ah, -an, -aj, al, } { bx, -bn, -ch, bg, -ce, -bq, bu, ca,-bk, -ck, bj, -cb, -bt, br, cd, -bh, ci, bm, -by, -bw, bo, cg, -bf, cf,bp, -bv, -bz, bl, cj, -bi, cc, bs, -bs, -cc, bi, -cj, -bl, bz, bv, -bp,-cf, bf, -cg, -bo, bw, by, -bm, -ci, bh, -cd, -br, bt, cb, -bj, ck, bk,-ca, -bu, bq, ce, -bg, ch, bn, -bx } { ay, -as, -be, ar, -az, -ax, at,bd, -aq, ba, aw, -au, -bc, ap, -bb, -av, av, bb, -ap, bc, au, -aw, -ba,ag, -bd, -at, ax, az, -ar, be, as, -ay, -ay, as, be, -ar, az, ax, -at,-bd, aq, -ba, -aw, au, bc, -ap, bb, av, -av, -bb, ap, -bc, -au, aw, ba,-aq, bd, at, -ax, -az, ar, -be, -as, ay } { by, -bk, cj, bn, -bv, -cb,bh, -cg, -bq, bs, ce, -bf, cd, bt, -bp, -ch, bi, -ca, -bw, bm, ck, -bl,bx, bz, -bj, ci, bo, -bu, -cc, bg, -cf, -br, br, cf, -bg, cc, bu, -bo,-ci, bj, -bz, -bx, bl, -ck, -bm, bw, ca, -bi, ch, bp, -bt, -cd, bf, -ce,-bs, bq, cg, -bh, cb, bv, -bn, -cj, bk, -by } { af, -ad, ag, ae, -ae,-ag, ad, -af, -af, ad, -ag, -ae, ae, ag, -ad, af, af, -ad, ag, ae, -ae,-ag, ad, -af, -af, ad, -ag, -ae, ae, ag, -ad, af, af, -ad, ag, ae, -ae,-ag, ad, -af, -af, ad, -ag, -ae, ae, ag, -ad, af, af, -ad, ag, ae, -ae,-ag, ad, -af, -af, ad, -ag, -ae, ae, ag, -ad, af } { bz, -bh, ce, bu,-bm, cj, bp, -br, -ch, bk, -bw, -cc, bf, -cb, -bx, bj, -cg, -bs, bo, ck,-bn, bt, cf, -bi, by, ca, -bg, cd, bv, -bl, ci, bq, -bq, -ci, bl, -bv,-cd, bg, -ca, -by, bi, -cf, -bt, bn, -ck, -bo, bs, cg, -bj, bx, cb, -bf,cc, bw, -bk, ch, br, -bp, -cj, bm, -bu, -ce, bh, -bz } { az, -ap, ba,ay, -aq, bb, ax, -ar, bc, aw, -as, bd, av, -at, be, au, -au, -be, at,-av, -bd, as, -aw, -bc, ar, -ax, -bb, aq, -ay, -ba, ap, -az, -az, ap,-ba, -ay, aq, -bb, -ax, ar, -bc, -aw, as, -bd, -av, at, -be, -au, au,be, -at, av, bd, -as, aw, bc, -ar, ax, bb, -aq, ay, ba, -ap, az } { ca,-bf, bz, cb, -bg, by, cc, -bh, bx, cd, -bi, bw, ce, -bj, bv, cf, -bk,bu, cg, -bl, bt, ch, -bm, bs, ci, -bn, br, cj, -bo, bq, ck, -bp, bp,-ck, -bq, bo, -cj, -br, bn, -ci, -bs, bm, -ch, -bt, bl, -cg, -bu, bk,-cf, -bv, bj, -ce, -bw, bi, -cd, -bx, bh, -cc, -by, bg, -cb, bz, bf, -ca} { am, -ah, al, an, -ai, ak, ao, -aj, aj, -ao, -ak, ai, -an, -al, ah,-am, -am, ah, -al, -an, ai, -ak, -ao, aj, -aj, ao, ak, -ai, an, al, -ah,am, am, -ah, al, an, -ai, ak, ao, -aj, aj, -ao, -ak, ai, -an, -al, ah,-am, -am, ah, -al, -an, ai, -ak, -ao, aj, -aj, ao, ak, -ai, an, al, -ah,am } { cb, -bi, bu, ci, -bp, bn, -cg, -bw, bg, -bz, -cd, bk, -bs, -ck,br, -bl, ce, by, -bf, bx, cf, -bm, bq, -cj, -bt, bj, -cc, -ca, bh, -bv,-ch, bo, -bo, ch, bv, -bh, ca, cc, -bj, bt, cj, -bq, bm, -cf, -bx, bf,-by, -ce, bl, -br, ck, ba, -bk, cd, bz, -bg, bw, cg, -bn, bp, -ci, -bu,bi, -cb } { ba, -ar, av, -be, -aw, aq, -az, -bb, as, -au, bd, ax, -ap,ay, bc, -at, at, -bc, -ay, ap, -ax, -bd, au, -as, bb, az, -aq, aw, be,-av, ar, -ba, -ba, ar, -av, be, aw, -aq, az, bb, -as, au, -bd, -ax, ap,-ay, -bc, at, -at, bc, ay, -ap, ax, bd, -au, as, -bb, -az, aq, -aw, -be,av, -ar, ba } { cc, -bl, bp, -cg, -by, bh, -bt, ck, bu, -bg, bx, ch,-bq, bk, -cb, -cd, bm, -bo, cf, bz, -bi, bs, -cj, -bv, bf, -bw, -ci, br,-bj, ca, ce, -bn, bn, -ce, -ca, bj, -br, ci, bw, -bf, bv, cj, -ba, bi,-bz, -cf, bo, -bm, cd, cb, -bk, bq, -ch, -bx, bg, -bu, -ck, bt, -bh, by,cg, -bp, bl, -cc } { ac, -ab, ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab,-ac, -ac, ab, -ab, ac, ac, -ab, ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab,-ac, -ac, ab, -ab, ac, ac, -ab, ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab,-ac, -ac, ab, -ab, ac, ac, -ab, ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab,-ac, -ac, ab, -ab, ac } { cd, -bo, bk, -bz, -ch, bs, -bg, bv, -ck, -bw,bh, -br, cg, ca, -bl, bn, -cc, -ce, bp, -bj, by, ci, -bt, bf, -bu, cj,bx, -bi, bq, -cf, -cb, bm, -bm, cb, cf, -bq, bi, -bx, -cj, bu, -bf, bt,-ci, -by, bj, -bp, ce, cc, -bn, bl, -ca, -cg, br, -bh, bw, ck, -bv, bg,-bs, ch, bz, -bk, bo, -cd } { bb, -au, aq, -ax, be, ay, -ar, at, -ba,-bc, av, -ap, aw, -bd, -az, as, -as, az, bd, -aw, ap, -av, bc, ba, -at,ar, -ay, -be, ax, -aq, au, -bb, -bb, au, -aq, ax, -be, -ay, ar, -at, ba,bc, -av, ap, -aw, bd, az, -as, as, -az, -bd, aw, -ap, av, -bc, -ba, at,-ar, ay, be, -ax, aq, -au, bb } { ce, -br, bf, -bs, cf, cd, -bq, bg,-bt, cg, cc, -bp, bh, -bu, ch, cb, -bo, bi, -bv, ci, ca, -bn, bj, -bw,cj, bz, -bm, bk, -bx, ck, by, -bl, bl, -by, -ck, bx, -bk, bm, -bz, -cj,bw, -bj, bn, -ca, -ci, bv, -bi, bo, -cb, -ch, bu, -bh, bp, -cc, -cg, bt,-bg, bq, -cd, -cf, ba, bf, br, -ce } { an, -ak, ah, -aj, am, ao, -al,ai, -ai, al, -ao, -am, aj, -ah, ak, -an, -an, ak, -ah, aj, -am, -ao, al,-ai, ai, -ai, ao, am, -aj, ah, -ak, an, an, -ak, ah, -aj, am, ao, -al,ai, -ai, al, -ao, -am, aj, -ah, ak, -an, -an, ak, -ah, aj, -am, -ao, al,-ai, ai, -al, ao, am, -aj, ah, -ak, an } { cf, -bu, bj, -bl, bw, -ch,-cd, bs, -bh, bn, by, cj, cb, -bq, bf, -bp, ca, ck, -bz, bo, -bg, br,-cc, -ci, bx, -bm, bi, -bt, ce, cg, -bv, bk, -bk, bv, -cg, -ce, bt, -bi,bm, -bx, ci, cc, -br, bg, -bo, bz, -ck, -ca, bp, -bf, bq, -cb, -cj, by,-bn, bh, -bs, cd, ch, -bw, bl, -bj, bu, -cf } { bc, -ax, as, -aq, av,-ba, -be, az, -au, ap, -at, ay, -bd, -bb, aw, -ar, ar, -aw, bb, bd, -ay,at, -ap, au, -az, be, ba, -av, aq, -as, ax, -bc, -bc, ax, -as, aq, -av,ba, be, -az, au, -ap, at, -ay, bd, bb, -aw, ar, -ar, aw, -bb, -bd, ay,-at, ap, -au, az, -be, -ba, av, -aq, as, -ax, bc } { cg, -bx, bo, -bf,bn, -bw, cf, ch, -by, bp, -bg, bm, -bv, ce, ci, -bz, bq, -bh, bl, -b u,cd, cj, -ca, br, -bi, bk, -b t, cc, ck, -cb, bs, -bj, bj, -bs, cb, -ck,-cc, bt, -bk, bi, -br, ca, -cj, -cd, bu, -bl, bh, -bq, bz, -ci, -ce, bv,-bm, bg, -bp, by, -ch, -cf, bw, -bn, bf, -bo, bx, -cg } { ag, -af, ae,-ad, ad, -ae, af, -ag, -ag, af, -ae, ad, -ad, ae, -af, ag, ag, -af, ae,-ad, ad, -ae, af, -ag, -ag, af, -ae, ad, -ad, ae, -af, ag, ag, -af, ae,-ad, ad, -ae, af, -ag, -ag, af, -ae, ad, -ad, ae, -af, ag, ag, -af, ae,-ad, ad, -ae, af, -ag, -ag, af, -ae, ad, -ad, ae, -af, ag } { ch, -ca,bt, -bm, bf, -bl, bs, -bz, cg, ci, -cb, bu, -bn, bg, -bk, br, -by, cf,cj, -cc, bv, -bo, bh, -bj, bq, -bx, ce, ck, -cd, bw, -bp, bi, -bi, bp,-bw, cd, -ck, -ce, bx, -bq, bj, -bh, bo, -bv, cc, -cj, -cf, by, -br, bk,-bg, bn, -bu, cb, -ci, -cg, bz, -bs, bl, -bf, bm, -bt, ca, -ch } { bd,-ba, ax, -au, ar, -ap, as, -av, ay, -bb, be, bc, -az, aw, -at, aq, -aq,at, -aw, az, -bc, -be, bb, -ay, av, -as, ap, -ar, au, -ax, ba, -bd, -bd,ba, -ax, au, -ar, ap, -as, av, -ay, bb, -be, -b c, az, -aw, at, -aq, aq,-at, aw, -az, bc, be, -bb, ay, -av, as, -ap, ar, -au, ax, -ba, bd } {ci, -cd, by, -bt, bo, -bj, bf, -bk, bp, -bu, bz, -ce, cj, ch, -cc, bx,-bs, bn, -bi, bg, -bl, bq, -bv, ca, -cf, ck, cg, -cb, bw, -br, bm, -bh,bh, -bm, br, -bw, cb, -cg, -ck, cf, -ca, bv, -bq, bl, -bg, bi, -bn, bs,-bx, cc, -ch, -cj, ce, -bz, bu, -bp, bk, -bf, bj, -bo, bt, -by, cd, -ci} { ao, -an, am, -al, ak, -aj, ai, -ah, ah, -ai, aj, -ak, al, -am, an,-ao, -ao, an, -am, al, -ak, aj, -ai, ah, -ah, ai, -aj, ak, -al, am, -an,ao, ao, -an, am, -al, ak, -aj, ai, -ah, ah, -ai, aj, -ak, al, -am, an,-ao, -ao, an, -am, al, -ak, aj, -ai, ah, -ah, ai, -aj, ak, -al, -am,-an, ao } { cj, -cg, cd, -ca, bx, -bu, br, -bo, bl, -bi, bf, -bh, bk,-bn, bq, -bt, bw, -bz, cc, -cf, ci, ck, -ch, ce, -cb, by, -bv, bs, -bp,bm, -bj, bg, -bg, bj, -bm, bp, -bs, bv, by, cb, -ce, ch, -ck, cf, -cc,bz, -bw, bt, -bq, bn, -bk, bh, -bf, bi, -bl, bo, -br, bu, -bx, ca, -cd,cg, -cj } { be, -bd, bc, -bb, ba, -az, ay, -ax, aw, -av, au, -at, as,-ar, aq, -ap, ap, -aq, ar, -as, at, -au, av, -aw, ax, -ay, az, -ba, bb,-bc, bd, -be, -be, bd, -bc, bb, -ba, az, -ay, ax, -aw, av, -au, at, -as,ar, -aq, ap, -ap, aq, -ar, as, -at, au, -av, aw, -ax, ay, -az, ba, -bb,bc, -bd, be } { ck, -cj, ci, -ch, cg, -cf, ce, -cd, cc, -cb, ca, -bz,by, -bx, bw, -bv, bu, -bt, bs, -br, bq, -bp, bo, -bn, bm, -bl, bk, -bj,bi, -bh, bg, -bf, bf, -bg, bh, -bi, bj, -bk, bl, -bm, bn, -bo, bp, -bq,br, -bs, bt, -bu, bv, -bw, bx, by, bz, -ca, cb, -cc, cd, -ce, cf, -cg,ch, -ci, cj, -ck } } where { aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak,al, am, an, ao, ap, aq, ar, as, at, au, ay, aw, ax, ay, az, ba, bb, be,bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu,by, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck} = 64,83, 36, 89, 75, 50, 18, 90, 87, 80, 70, 57, 43, 25, 9, 90, 90, 88, 85,82, 78, 73, 67, 61, 54, 46, 38, 31, 22, 13, 4, 9 1, 90, 90, 90, 88, 87,86, 84, 83, 81, 79, 77, 73, 71, 69, 65, 62, 59, 56, 52, 48, 44, 41, 37,33, 28, 24, 20, 15, 11, 7, 2

In addition to DCT-2 and 4×4 DST-7 which have been employed in HEVC, anAdaptive Multiple Transform (AMT, or as known as Enhanced MultipleTransform (EMT), or as known as Multiple Transform Selection (MTS))scheme has been used in VVC for residual coding for both inter and intracoded blocks. The MTS uses multiple selected transforms from the DCT/DSTfamilies other than the current transforms in HEVC. The newly introducedtransform matrices are DST-7, DCT-8. Table 1 shows the basis functionsof the selected DST/DCT.

TABLE 1 Transform basis functions of DCT-2, DST-7 and DCT-8 for N-pointinput Transform Type Basis function T_(i)(j), i, j = 0, 1, . . . , N − 1DCT-2${T_{i}(j)} = {{\omega_{0} \cdot \sqrt{\frac{2}{N}} \cdot \cos}\;\left( \frac{\pi \cdot i \cdot \left( {{2j} + 1} \right)}{2N} \right)}$${{where}\mspace{14mu}\omega_{0}} = \left\{ \begin{matrix}\sqrt{\frac{2}{N}} & {i = 0} \\1 & {i \neq 0}\end{matrix} \right.$ DCT-8${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\cos\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {{2j} + 1} \right)}{{4N} + 2} \right)}}$DST-7${T_{i}(j)} = {\sqrt{\frac{4}{{2N} + 1}} \cdot {\sin\left( \frac{\pi \cdot \left( {{2i} + 1} \right) \cdot \left( {j + 1} \right)}{{2N} + 1} \right)}}$

All the primary transform matrices in VVC are used with 8-bitrepresentation. The AMT applies to the CUs with both width and heightsmaller than or equal to 32, and whether applying AMT or not iscontrolled by a flag called mts flag. When the mts flag is equal to 0,only DCT-2 is applied for coding the residue. When the mts flag is equalto 1, an index mts_idx is further signalled using 2 bins to specify thehorizontal and vertical transform to be used according to Table 2, wherevalue 1 means using DST-7 and value 2 means using DCT-8.

TABLE 2 Specification of trTypeHor and trTypeVer depending on mts_idx[ x][ y ][ cIdx ] mts_idx[ xTbY ][ yTbY ][ cIdx ] trTypeHor trTypeVer −1 00 0 1 1 1 2 1 2 1 2 3 2 2The transform core, which is a matrix composed by the basis vectors, ofDST-7 can be also represented below:

4-point DST-7: { a, b, c, d } { c, c, 0, -c } { d, -a, -c, b } { b, -d,c, -a } where {a, b, c, d} = { 29, 55, 74, 84}. 8-point DST-7: { a, b,c, d, e, f, g, h,} { c, f, h, e, b, -a, -d, -g,} { e, g, b, -c, -h, -d,a, f,} { g, c, -d, -f, a, h, b, -e,} { h, -a, -g, b, f, -c, -e, d,} { f,-e, -a, g, -d, -b, h, -c,} { d, -h, e, -a, -c, g, -f, b,} { b, -d, f,-h, g, -e, c, -a,} where {a, b, c, d, e, f, g, h} = { 17, 32, 46, 60,71, 78, 85, 86}. 16-point DST-7: { a, b, c, d, e, f, g, h, i, j, k, l,m, n, o, p,} { c, f, i, l, o, o, l, i, f, c, 0, -c, -f, -i, -l, -o,} {e, j, o, m, h, c, -b, -g, -l, -p, -k, -f, -a, d, i, n,} { g, n, l, e,-b, -i, -p, -j, -c, d, k, o, h, a, -f, -m,} { i, o, f, -c, -l, -l, -c,f, o, i, 0, -i, -o, -f, c, l,} { k, k, 0, -k, -k, 0, k, k, 0, -k, -k, 0,k, k, 0, -k,} { m, g, -f, -n, -a, l, h, -e, -o, -b, k, i, -d, -p, -c,j,} { o, c, -l, -f, i, i, -f, -l, c, o, 0, -o, -c, l, f, -i,} { p, -a,-o, b, n, -c, -m, d, l, -e, -k, f, j, -g, -i, h,} { n, -e, -i, j, d, -o,a, m, -f, -h, k, c, -p, b, l, -g,} { l, -i, -c, o, -f, -f, o, -c, -i, l,0, -l, i, c, -o, f,} { j, -m, c, g, -p, f, d, -n, i, a, -k, l, -b, -h,o, -e,} { h, -p, i, -a, -g, o, -j, b, f, -n, k, -c, -e, m, -l, d,} { f,-l, o, -i, c, c, -i, o, -l, f, 0, -f, l, -o, i, -c,} { d, -h, l, -p, m,-i, e, -a, -c, g, -k, o, -n, j, -f, b,} { b, -d, f, -h, j, -l, n, -p, o,-m, k, -i, g, -e, c, -a,} where {a, b, c, d, e, f, g, h, i, j, k, l, m,n, o, p} = { 9, 17, 25, 33, 41, 49, 56, 62, 66, 72, 77, 81, 83, 87, 89,90}. 32 -point DST-7: { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p,q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F} { c, f, i, l, o, r, u,x, A, D, F, C, z, w, t, q, n, k, h, e, b, -a, -d, -g, -j, -m, -p, -s,-v, -y, -B, -E,} { e, j, o, t, y, D, D, y, t, o, j, e, 0, -e, -j, -o,-t, -y, -D, -D, -y, -t, -o, -j, -e, 0, e, j, o, t, y, D,} { g, n, u, B,D, w, p, i, b, -e, -l, -s, -z, -F, -y, -r, -k, -d, c, j, q, x, E, A, t,m, f, -a, -h, -o, -v, -C,} { i, r, A, C, t, k, b, -g, -p, -y, -E, -v,-m, -d, e, n, w, F, x, o, f, -c, −l, -u, -D, -z, -q, -h, a, j, s, B,} {k, v, F, u, j, -a, −l, -w, -E, -t, -i, b, m, x, D, s, h, -c, -n, -y, -C,-r, -g, d, o, z, B, q, f, -e, -p, -A} { m, z, z, m, 0, -m, -z, -z, -m,0, m, z, z, m, 0, -m, -z, -z, -m, 0, m, z, z, m, 0, -m, -z, -z, -m, 0,m, z,} { o, D, t, e, -j, -y, -y, -j, e, t, D, o, 0, -o, -D, -t, -e, j,y, y, j, -e, -t, -D, -o, 0, o, D, t, e, -j, -y,} { q, E, n, -c, -t, -B,-k, f, w, y, h, -i, -z, -v, -e, l, C, s, b, -o, -F, -p, a, r, D, m, -d,-u, -A, -j, g, x,} { s, A, h, -k, -D, -p, c, v, x, e, -n, -F, -m, f, y,u, b, -q, -C, -j, i, B, r, -a, -t, -z, -g, l, E, o, -d, -w,} { u, w, b,-s, -y, -d, q, A, f, -o, -C, -h, m, E, j, -k, -F, -l, i, D, n, -g, -B,-p, e, z, r, -c, -x, -t, a, v,} { w, s, -d, -A, -o, h, E, k, -l, -D, -g,p, z, c, -t, -v, a, x, r, -e, -B, -n, i, F, j, -m, -C, -f, q, y, b, -u,}{ y, o, -j, -D, -e, t, t, -e, -D, -j, o, y, 0, -y, -o, j, D, e, -t, -t,e, D, j, -o, -y, 0, y, o, -j, -D, -e, t,} { A, k, -p, -v, e, F, f, -u,-q, j, B, a, -z, -l, o, w, -d, -E, -g, t, r, -i, -C, -b, y, m, -n, -x,c, D, h, -s,} { C, g, -v, -n, o, u, -h, -B, a, D, f, -w, -m, p, t, -i,-A, b, E, e, -x, -l, q, s, -j, -z, c, F, d, -y, -k, r,} { E, c, -B, -f,y, i, -v, -l, s, o, -p, -r, m, u, -j, -x, g, A, -d, -D, a, F, b, -C, -e,z, h, -w, -k, t, n, -q,} { F, -a, -E, b, D, -c, -C, d, B, -e, -A, f, z,-g, -y, h, x, -i, -w, j, v, -k, -u, l, t, -m, -s, n, r, -o, -q, p,} { D,-e, -y, j, t, -o, -o, t, j, -y, -e, D, 0, -D, e, y, -j, -t, o, o, -t,-j, y, e, -D, 0, D, -e, -y, j, t, -o,} { B, -i, -s, r, j, -A, -a, C, -h,-t, q, k, -z, -b, D, -g, -u, p, l, -y, -c, E, -f, -v, o, m, -x, -d, F,-e, -w, n,} { z, -m, -m, z, 0, -z, m, m, -z, 0, z, -m, -m, z, 0, -z, m,m, -z, 0, z, -m, -m, z, 0, -z, m, m, -z, 0, z, -m,} { x, -q, -g, E, -j,-n, A, -c, -u, t, d, -B, m, k, -D, f, r, -w, -a, y, -p, -h, F, -i, -o,z, -b, -v, s, e, -C, l,} { v, -u, -a, w, -t, -b, x, -s, -c, y, -r, -d,z, -q, -e, A, -p, -f, B, -o, -g, C, -n, -h, D, -m, -i, E, -l, -j, F,-k,} { t, -y, e, o, -D, j, j, -D, o, e, -y, t, 0, -t, y, -e, -o, D, -j,-j, D, -o, -e, y, -t, 0, t, -y, e, o, -D, j,} { r, -C, k, g, -y, v, -d,-n, F, -o, -c, u, -z, h, j, -B, s, -a, -q, D, -l, -f, x, -w, e, m, -E,p, b, -t, A, -i,} { p, -F, q, -a, -o, E, -r, b, n, -D, s, -c, -m, C, -t,d, l, -B, u, -e, -k, A, -v, f, j, -z, w, -g, -i, y, -x, h,} { n, -B, w,-i, -e, s, -F, r, -d, -j, x, -A, m, a, -o, C, -v, h, f, -t, E, -q, c, k,-y, z, -l, -b, p, -D, u, -g,} { l, -x, C, -q, e, g, -s, E, -v, j, b, -n,z, -A, o, -c, -i, u, -F, t, -h, -d, p, -B, y, -m, a, k, -w, D, -r, f, }{ j, -t, D, -y, o, -e, -e, o, -y, D, -t, j, 0, -j, t, -D, y, -o, e, e,-o, y, -D, t, -j, 0, j, -t, D, -y, o, -e,} { h, -p, x, -F, y, -q, i, -a,-g, o, -w, E, -z, r, -j, b, f, -n, v, -D, A, -s, k, -c, -e, m, -u, C,-B, t, -l, d,} { f, -l, r, -x, D, -C, w, -q, k, -e, -a, g, -m, s, -y, E,-B, v, -p, j, -d, -b, h, -n, t, -z, F, -A, u, -o, i, -c,} { d, -h, l,-p, t, -x, B, -F, C, -y, u, -q, m, -i, e, -a, -c, g, -k, o, -s, w, -A,E, -D, z, -v, r, -n, j, -f, b,} { b, -d, f, -h, j, -l, n, -p, r, -t, v,-x, z, -B, D, -F, E, C, A, -y, w, -u, s, -q, o, -m, k, -i, g, -e, c,-a,} where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t,u, v, w, x, y, z, A, B, C, D, E, F } = { 4, 9, 13, 17, 21, 26, 30, 34,38, 42, 45, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85,86, 88, 88, 89, 90, 90 }. 4-point DCT-8: { a, b, c, d,} { b, 0, -b, -b,}{ c, -b, -d, a,} { d, -b, a, -c,} where {a, b, c, d} = { 84, 74, 55,29}. 8-point DCT-8: { a, b, c, d, e, f, g, h,} { b, e, h, -g, -d, -a,-c, -f,} { c, h, -e, -a, -f, g, b, d,} { d, -g, -a, -h, c, e, -f, -b} {e, -d, -f, c, g, -b, -h, a,} { f, -a, g, e, -b, h, d, -c,} { g, -c, b,-f, -h, d, -a, e,} { h, -f, d, -b, a, -c, e, -g,} where {a, b, c, d, e,f, g, h} = { 86, 85, 78, 71, 60, 46, 32, 17}. 16 -point DCT-8: { a, b,c, d, e, f, g, h, i, j, k, l, m, n, o, p,} { b, e, h, k, n, 0, -n, -k,-h, -e, -b, -b, -e, -h, -k, -n,} { c, h, m, -p, -k, -f, -a, -e, -j, -o,n, i, d, b, g, l,} { d, k, -p, -i, -b, -f, -m, n, g, a, h, o, -l, -e,-c, -j,} { e, n, -k, -b, -h, 0, h, b, k, -n, -e, -e, -n, k, b, h,} { f,0, -f, -f, 0, f, f, 0, -f, -f, 0, f, f, 0, -f, -f,} { g, -n, -a, -m, h,f, -o, -b, -l, i, e, -p, -c, -k, j, d,} { h, -k, -e, n, b, 0, -b, -n, e,k, -h, -h, k, e, -n, -b,} { i, -h, -j, g, k, -f, -l, e, m, -d, -n, c, o,-b, -p, a,} { j, -e, -o, a, -n, -f, i, k, -d, -p, b, -m, -g, h, l, -c,}{ k, -b, n, h, -e, 0, e, -h, -n, b, -k, -k, b, -n, -h, e,} { l, -b, i,o, -e, f, -p, -h, c, -m, -k, a, -j, -n, d, -g,} { m, -e, d, -l, -n, f,-c, k, o, -g, b, -j, -p, h, -a, i,} { n, -h, b, -e, k, 0, -k, e, -b, h,-n, -n, h, -b, e, -k,} { o, -k, g, -c, b, -f, j, -n, -p, l, -h, d, -a,e, -i, m,} { p, -n, l, -j, h, -f, d, -b, a, -c, e, -g, i, -k, m, -o,}where {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} = { 90, 89, 87,83, 81, 77, 72, 66, 62, 56, 49, 41, 33, 25, 17, 9}. 32-point DCT-8: { a,b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,z, A, B, C, D, E, F,} { b, e, h, k, n, q, t, w, z, C, F, -E, -B, -y, -v,-s, -p, -m, -j, -g, -d, -a, -c, -f, -i, -l, -o, -r, -u, -x, -A, -D,} {c, h, m, r, w, B, 0, -B, -w, -r, -m, -h, -c, -c, -h, -m, -r, -w, -B, 0,B, w, r, m, h, c, c, h, m, r, w, B} { d, k, r, y, F, -A, -t, -m, -f, -b,-i, -p, -w, -D, C, v, o, h, a, g, n, u, B, -E, -x, -q, -j, -c, -e, -l,-s, -z,} { e, n, w, F, -y, -p, -g, -c, -l, -u, -D, A, r, i, a, j, s, B,-C, -t, -k, -b, -h, -q, -z, E, v, m, d, f, o, x,} { f, q, B, -A, -p, -e,-g, -r, -C, z, o, d, h, s, D, -y, -n, -c, -i, -t, -E, x, m, b, j, u, F,-w, -l, -a, -k, -v,} { g, t, 0, -t, -g, -g, -t, 0, t, g, g, t, 0, -t,-g, -g, -t, 0, t, g, g, t, 0, -t, -g, -g, -t, 0, t, g, g, t,} { h, w,-B, -m, -c, -r, 0, r, c, m, B, -w, -h, -h, -w, B, m, c, r, 0, -r, -c,-m, -B, w, h, h, w, -B, -m, -c, -r,} { i, z, -w, -f, -l, -C, t, c, o, F,-q, -a, -r, E, n, d, u, -B, -k, -g, -x, y, h, j, A, -v, -e, -m, -D, s,b, p,} { j, C, -r, -b, -u, z, g, m, F, -o, -e, -x, w, d, p, -E, -l, -h,-A, t, a, s, -B, -i, -k, -D, g, c, v, -y, -f, -n} { k, F, -m, -i, -D, o,g, B, -q, -e, -z, s, c, x, -u, -a, -v, w, b, t, -y, -d, -r, A, f, p, -C,-h, -n, E, j, l,} { l, -E, -h, -p, A, d, t, -w, -a, -x, s, e, B, -o, -i,-F, k, m, -D, -g, -q, z, c, u, -v, -b, -y, r, f, C, -n, -j,} { m, -B,-c, -w, r, h, 0, -h, -r, w, c, B, -m, -m, B, c, w, -r, -h, 0, h, r, -w,-c, -B, m, m, -B, -c, -w, r, h,} { n, -y, -c, -D, i, s, -t, -h, E, d, x,-o, -m, z, b, C, -j, -r, u, g, -F, -e, -w, p, l, -A, -a, -B, k, q, -v,-f,} { o, -v, -h, C, a, D, -g, -w, n, p, -u, -i, B, b, E, -f, -x, m, q,-t, -j, A, c, F, -e, -y, l, r, -s, -k, z, d,} { p, -s, -m, v, j, -y, -g,B, d, -E, -a, -F, c, C, -f, -z, i, w, -l, -t, o, q, -r, -n, u, k, -x,-h, A, e, -D, -b,} { q, -p, -r, o, s, -n, -t, m, u, -l, -v, k, w, -j,-x, i, y, -h, -z, g, A, -f, -B, e, C, -d, -D, c, E, -b, -F, a,} { r, -m,-w, h, B, -c, 0, c, -B, -h, w, m, -r, -r, m, w, -h, -B, c, 0, -c, B, h,-w, -m, r, r, -m, -w, h, B, -c,} { s, -j, -B, a, -C, -i, t, r, -k, -A,b, -D, -h, u, q, -l, -z, c, -E, -g, v, p, -m, -y, d, -F, -f, w, o, -n,-x, e,} { t, -g, 0, g, -t, -t, g, 0, -g, t, t, -g, 0, g, -t, -t, g, 0,-g, t, t, -g, 0, g, -t, -t, g, 0, -g, t, t, -g,} { u, -d, B, n, -k, -E,g, -r, -x, a, -y, -q, h, -F, -j, o, A, -c, v, t, -e, C, m, -l, -D, f,-s, -w, b, -z, -p, i,} { v, -a, w, u, -b, x, t, -c, y, s, -d, z, r, -e,A, q, -f, B, p, -g, C, o, -h, D, n, -i, E, m, -j, F, l, -k,} { w, -c, r,B, -h, m, 0, -m, h, -B, -r, c, -w, -w, c, -r, -B, h, -m, 0, m, -h, B, r,-c, w, w, -c, r, B, -h, m,} { x, -f, m, -E, -q, b, -t, -B, j, -i, A, u,-c, p, F, -n, e, -w, -y, g, -l, D, r, -a, s, C, -k, h, -z, -v, d, -o,} {y, -i, h, -x, -z, j, -g, w, A, -k, f, -v, -B, l, -e, u, C, -m, d, -t,-D, n, -c, s, E, -o, b, -r, -F, p, -a, q,} { z, -l, c, -q, E, u, -g, h,-v, -D, p, -b, m, -A, -y, k, -d, r, -F, -t, f, -i, w, C, -o, a, -n, B,x, -j, e, -s,} { A, -o, c, -j, v, F, -t, h, -e, q, -C, -y, m, -a, l, -x,-D, r, -f, g, -s, E, w, -k, b, -n, z, B, -p, d, -i, u,} { B, -r, h, -c,m, -w, 0, w, -m, c, -h, r, -B, -B, r, -h, c, -m, w, 0, -w, m, -c, h, -r,B, B, -r, h, -c, m, -w,} { C, -u, m, -e, d, -l, t, -B, -D, v, -n, f, -c,k, -s, A, E, -w, o, -g, b, -j, r, -z, -F, x, -p, h, -a, i, -q, y,} { D,-x, r, -l, f, -a, g, -m, s, -y, E, C, -w, q, -k, e, -b, h, -n, t, -z, F,B, -v, p, -j, d, -c, i, -o, u, -A,} { E, -A, w, -s, o, -k, g, -c, b, -f,j, -n, r, -v, z, -D, -F, B, -x, t, -p, l, -h, d, -a, e, -i, m, -q, u,-y, C,} { F, -D, B, -z, x, -v, t, -r, p, -n, l, -j, h, -f, d, -b, a, -c,e, -g, i, -k, m, -o, q, -s, u, -w, y, -A, C, -E,} where {a, b, c, d, e,f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C,D E F } = {90, 90, 89, 88, 88, 86, 85, 84, 82, 80, 78, 77, 74, 72, 68,66, 63, 60, 56, 53, 50, 45, 42, 38, 34, 30, 26, 21, 17, 13, 9, 4}.

In VCC, an Intra Sub-Partitions (ISP) coding mode divides lumaintra-predicted blocks vertically or horizontally into 2 or 4sub-partitions depending on the block size dimensions, as shown in Table3. FIG. 9 and FIG. 10 show examples of the two possibilities. FIG. 9illustrates an exemplary division of a 4×8 block or a 8×4 block. FIG. 10illustrate an exemplary division of a block that is not one of a 4×8block, a 8×4 bock, or a 4×4 block. All sub-partitions fulfill thecondition of having at least 16 samples. For chroma components, ISP isnot applied.

TABLE 3 Number of sub-partitions depending on the block size Block SizeNumber of Sub-Partitions 4 × 4 Not divided 4 × 8 and 8 × 4 2 All othercases 4

For each of these sub-partitions, a residual signal is generated byentropy decoding the coefficients sent by the encoder and then inversequantizing and inverse transforming the coefficients. Then, thesub-partition is intra predicted and finally the correspondingreconstructed samples are obtained by adding the residual signal to theprediction signal. Therefore, the reconstructed values of eachsub-partition can be available to generate the prediction of the nextone, which can repeat the process and so on. All sub-partitions sharethe same intra mode.

In some embodiments, the ISP algorithm will only be tested with intramodes that are part of the MPM list. For this reason, if a block usesISP, then the MPM flag will be inferred to be one. Besides, if ISP isused for a certain block, then the MPM list will be modified to excludethe DC mode and to prioritize horizontal intra modes for the ISPhorizontal split and vertical intra modes for the vertical one.

In ISP, each sub-partition can be regarded as a sub-TU, since thetransform and reconstruction is performed individually for eachsub-partition. The related syntax elements signaled for ISP are shown intable 4.

TABLE 4 Syntax elements signaled for ISP Descriptor coding_unit( x0, y0,cbWidth, cbHeight, treeType ) { if( tile_group_type != I ||sps_ibc_enabled_flag ) { if( treeType != DUAL_TREE_CHROMA )cu_skip_flag[ x0 ] [ y0 ] ae(v) if( cu_skip_flag[ x0 ] [ y0 ] = = 0 &&tile_group_type != I ) pred_mode_flag ae(v) if( ( ( tile_group_type = =I && cu_skip_flag[ x0 ][ y0 ] = =0 ) || ( tile_group_type != I &&CuPredMode[ x0 ][ y0 ] != MODE_INTRA ) ) && sps_ibc_enabled_flag )pred_mode_ibc_flag ae(v) } if( CuPredMode[ x0 ][ y0 ] = = MODE_INTRA ) {if( sps_pcm_enabled_flag && cbWidth >= MinIpcmCbSizeY && cbWidth <=MaxIpcmCbSizeY && cbHeight >= MinIpcmCbSizeY && cbHeight <=MaxIpcmCbSizeY ) pcm_flag[ x0 ][ y0 ] ae(v) if( pcm_flag[ x0 ][ y0 ]) {while( !byte_aligned( ) ) pcm_alignment_zero_bit f(1) pcm_sample(cbWidth, cbHeight, treeType) } else { if( treeType = = SINGLE_TREE | |treeType = = DUAL_TREE_LUMA ) { if( ( y0 % CtbSizeY ) > 0 )intra_luma_ref_idx[ x0 ][ y0 ] ae(v) if (intra_luma_ref_idx[ x0 ][ y0 ]= = 0 && ( cbWidth <= MaxTbSizeY | | cbHeight <= MaxTbSizeY ) && (cbWidth * cbHeight > MinTbSizeY * MinTbSizeY ))intra_subpartitions_mode_flag[ x0 ][ y0 ] ae(v) if(intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 1 && cbWidth <= MaxTbSizeY&& cbHeight <= MaxTbSizeY ) intra_subpartitions_split_flag[ x0 ][ v0 ]ae(v) if( intra_luma_ref_idx[ x0 ][ y0 ] = = 0 &&intra_subpartitions_mode_flag[ x0 ][ y0 ] = = 0 ) intra_luma_mpm_flag[x0 ][ y0 ] ae(v) if( intra_luma_mpm_flag[ x0 ] [ y0 ] )intra_luma_mpm_idx[ x0 ][ y0 ] ae(v) Else intra_luma_mpm_remainder[ x0][ y0 ] ae(v) } if( treeType = = SINGLE_TREE | | treeType = =DUAL_TREE_CHROMA ) intra_chroma_pred_mode[ x0 ][ y0 ] ae(v) } } else if(treeType != DUAL_TREE_CHROMA ) { /* MODE_INTER or MODE_IBC */ ...... }

In JVET-J0024, JVET-K0139 and JVET-L0358, a spatially varying transform(SVT) scheme is proposed. With SVT, for inter prediction residuals,there is only residual block in the coding block, but the residual blockis smaller than the coding block, therefore the transform size in SVT issmaller than the coding block size. For the region which is not coveredby the residual block or transform, zero residual is assumed.

More specifically, in JVET-L0358, SVT may also be called Sub-blockTransform (SBT). The sub-block types (SVT-H, SVT-V), sizes and positions(Left half, left quarter, right half, right quarter, top half, topquarter, bottom half, bottom quarter) supported in SBT can be shown inFIGS. 11A-11D. FIGS. 11A-11D illustrate the sub-block types (SVT-H,SVT-V), and the positions (Left half, right half, top half, bottom half)supported in SBT respectively. The shaded region labeled by a letter “A”is a residual block with transform, and the other region is assumed tobe zero residual without transform.

One problem with the SBT methods is that these methods requireadditional overhead bits (e.g., cu_sbt_flag, cu_sbt_quad_flag,cu_sbt_horizontal_flag, cu_sbt_pos_flag) to be signaled to indicate thesub-block type (horizontal or vertical), size (half or quarter) andposition (left or right, top or bottom). Tables 5-11 and texts infollowing paragraphs illustrate the proposed SBT.

TABLE 5 Sequence parameter set RBSP syntax Descriptorseq_parameter_set_rbsp( ) { sps_seq_parameter_set_id ue(v) ...sps_mts_intra_enabled_flag u(1) sps_mts_inter_enabled_flag u(1)sps_sbt_enable_flag u(1) rbsp_trailing_bits( ) }

TABLE 6 General slice header syntax Descriptor slice_header( ) {slice_pic_parameter_set_id ue(v) slice_address u(v) slice_type ue(v) if( slice_type != I ) { log2_diff_ctu_max_bt_size ue(v) if(sps_sbtmvp_cnabled_flag ) { sbtmvp_size_override_flag u(1) if(sbtmvp_size_override_flag)  1og2_sbtmvp_active_size_minus2 u(3) } if(sps_temporal_mvp_enabled_flag ) slice_temporal_mvp_enabled_flag u(1) if(slice_type = = B ) mvd_l1_zero_flag u(1) if(slice_temporal_mvp_enabled_flag ) { if( slice_type = = B ) collocated_from_l0_flag u(1) } six_minus_max_num_merge_cand ue(v) if(sps_sbt_enable_flag ) slice_max_sbt_size_64_flag u(1) } if (sps_alf_enabled_flag ) { slice_alf_enabled_flag u(1) if(slice_alf_enabled_flag ) alf_data( ) } dep_quant_enabled_flag u(1) if(!dep_quant_enabled_flag ) sign_data_hiding_enabled_flag u(1)byte_alignment( ) }

TABLE 7 Coding unit syntax Descriptor coding_unit( x0, y0, cbWidth,cbHeight, treeType ) { ... if( CuPredMode[ x0 ][ y0 ] != MODE_INTRA &&cu_skip_flag[ x0 ][ y0 ] = = 0 ) cu_cbf ae(v) if( cu_cbf) { if(CuPredMode[ x0 ][y0 ] != MODE_INTRA && sps_sbt_enable_flag ) { if(cbWidth <= maxSbtSize && cbHeight <= maxSbtSize ) {  allowSbtVerHalf =cbWidth >= 8  allowSbtVerQuad = cbWidth >= 16  allowSbtHorHalf =cbHeight >= 8  allowSbtHorQuad = cbHeight >= 16  if( allowSbtVerHalf | |allowSbtHorHalf | | allowSbtVerQuad | | allowSbtHorQuad ) cu_sbt_flag[x0 ] [ y0 ] ae(v) } if( cu_sbt_flag[ x0 ] [ y0 ] ) {  if( (allowSbtVerHalf | | allowSbtHorHalf ) && ( allowSbtVerQuad | |allowSbtHorQuad ) ) cu_sbt_quad_flag[ x0 ][ y0 ] ae(v) if((cu_sbt_quad_flag[ x0 ][ y0 ] && allowSbtVerQuad && allowSbtHorQuad ) || ( !cu_sbt_quad_flag[ x0 ][ y0 ] && allowSbtVerHalf && allowSbtHorHalf) ) cu_sbt_horizontal_flag[ x0 ] [ y0 ] ae(v)  cu_sbt_pos_flag[ x0 ][ y0] ae(v) } } transform_tree( x0, y0, cbWidth, cbHeight, treeType ) } }

TABLE 8 Transform tree syntax Descriptor transform_tree( x0, y0,tbWidth, tbHeight, treeType) { if( tbWidth > MaxTbSizeY | | tbHeight >MaxTbSizeY ) { trafoWidth = ( tbWidth > MaxTbSizeY ) ? (tbWidth / 2) :tbWidth trafoHeight = ( tbHeight > MaxTbSizeY ) ? (tbHeight / 2) :tbHeight transform_tree( x0, y0, trafoWidth, trafoHeight ) if( tbWidth >MaxTbSizeY ) transform_tree( x0 + trafoWidth, y0, trafoWidth,trafoHeight, treeType ) if( tbHeight > MaxTbSizeY ) transform tree( x0.y0 + trafoHeight, trafoWidth, trafoHeight, treeType ) if( tbWidth >MaxTbSizeY && tbHeight > MaxTbSizeY ) transform_tree( x0 + trafoWidth,y0 + trafoHeight, trafoWidth, trafoHeight, treeType ) } else if(cu_sbt_flag[ x0 ] [ y0 ] ) factorTb0 = cu_sbt_quad_flag[ x0 ] [ y0 ] ? 1: 2 factorTb0 = cu_sbt_pos_flag[ x0 ][ y0 ] ? ( 4 - factorTb0 ) :factorTb0 noResiTb0 = cu_sbt_pos_flag[ x0 ] [ y0 ] ? 1 : 0 if(!cu_sbt_horizontal_flag[ x0 ][ y0 ]) { trafoWidth = tbWidth * factorTb0/ 4 transform_tree( x0, y0, trafoWidth, tbHeight, treeType , noResiTb0 )transform_tree( x0 + trafoWidth, y0, tbWidth − trafoWidth, tbHeight,treeType ,  !noResiTb0) } else { trafoHeight = tbHeight * factorTb0 / 4transform_tree( x0, y0, tbWidth, trafoHeight, treeType , noResiTb0 )transform_tree( x0, y0 + trafoHeight, tbWidth, tbHeight − trafoHeight,treeType ,  !noResiTb0 ) } } else { transform_unit( x0, y0, tbWidth,tbHeight, treeType , 0 ) } }

TABLE 9 Transform unit syntax Descriptor transform_unit( x0, y0,tbWidth, tbHeight, treeType , noResi) { if( ( treeType = = SINGLE_TREE || treeType = = DUAL_TREE_LUMA) && !noResi ) tu_cbf_luma[ x0 ][ y0 ]ae(v) if( ( treeType = = SINGLE_TREE | | treeType = = DUAL_TREE_CHROMA )&& !noResi ) { tu_cbf_cb[ x0 ][ y0 ] ae(v) tu_cbf_cr[ x0 ][ y0 ] ae(v) }if( ( ( ( CuPredMode[ x0 ][ y0 ] = = MODE_INTRA) &&sps_mts_intra_enabled_flag ) | |  ( ( CuPredMode[ x0 ][ y0 ] = =MODE_INTER) && sps_mts_inter_enabled_flag ) )  && tu_cbf_luma[ x0 ][ y0] && treeType ! = DUAL_TREE_CHROMA  && ( tbWidth <= 32 ) && (tbHeight <=32 ) && !cu_sbt_flag[ x0 ][ y0 ] ) cu_mts_flag[ x0 ][ y0 ] ae(v) if(tu_cbf_luma[ x0 ][ y0 ] ) residual_coding( x0, y0. log2( tbWidth ),log2( tbHeight ), 0 ) if( tu_cbf_cb[ x0 ][ y0 ] ) residual_coding( x0.y0. log2( tbWidth / 2 ), log2( tbHeight / 2 ), 1 ) if( tu_cbf_cr[ x0 ] [y0 ] ) residual_coding( x0, y0, log2( tbWidth / 2 ), log2( tbHeight / 2), 2 ) }

Sequence Parameter Set RBSP Semantics

sps_sbt_enabled_flag equal to 0 specifies that sub-block transform forinter-predicted CU is disabled. sps_sbt_enabled_flag equal to 1specifies that sub-block transform for inter-predicted CU is enabled.

General Slice Header Semantics

slice_sbt_max_size_64_flag equal to 0 specifies that the maximum CUwidth and height for allowing sub-block transform is 32.slice_sbt_max_size_64_flag equal to 1 specifies that the maximum CUwidth and height for allowing sub-block transform is 64.

maxSbtSize=slice_sbt_max_size_64_flag? 64:32

Coding Unit Semantics

cu_sbt_flag[x0][y0] equal to 1 specifies that for the current codingunit, sub-block transform is used. cu_sbt_flag[x0][y0] equal to 0specifies that for the current coding unit, the sub-block transform isnot used.

When cu_sbt_flag[x0][y0] is not present, its value is inferred to beequal to 0.

When sub-block transform is used, a coding unit is tiled into twotransform units, one transform unit has residual block, the other doesnot have residual block.

cu_sbt_quad_flag[x0][y0] equal to 1 specifies that for the currentcoding unit, the sub-block transform include a transform unit of ¼ sizeof the current coding unit. cu_sbt_quad_flag[x0][y0] equal to 0specifies that for the current coding unit the sub-block transforminclude a transform unit of ½ size of the current coding unit.

When cu_sbt_quad_flag[x0][y0] is not present, its value is inferred tobe equal to 0.

cu_sbt_horizontal_flag[x0][y0] equal to 1 specifies that the currentcoding unit is tiled into 2 transform units by a horizontal split.cu_sbt_horizontal_flag[x0][y0] equal to 0 specifies that the currentcoding unit is tiled into 2 transform units by a vertical split.

When cu_sbt_horizontal_flag[x0][y0] is not present, its value is derivedas follows:

(a) If cu_sbt_quad_flag[x0][y0] is equal to 1,cu_sbt_horizontal_flag[x0][y0] is set to be equal to allowSbtHoriQuad.

(b) Otherwise (cu_sbt_quad_flag[x0][y0] is equal to 0),cu_sbt_horizontal_flag[x0][y0] is set to be equal to allowSbtHoriHalf.

cu_sbt_pos_flag[x0][y0] equal to 1 specifies that the tu_cbf_luma,tu_cbf_cb and tu_cbf_cr of the first transform unit in the currentcoding unit are not present in the bitstream. cu_sbt_pos_flag[x0][y0]equal to 0 specifies that the tu_cbf_luma, tu_cbf_cb and tu_cbf_cr ofthe second transform unit in the current coding unit are not present inthe bitstream.

Transformation process for scaled transform coefficients

Inputs to this Process are:

-   -   a luma location (xTbY, yTbY) specifying the top-left sample of        the current luma transform block relative to the top-left luma        sample of the current picture,    -   a variable nTbW specifying the width of the current transform        block,    -   a variable nTbH specifying the height of the current transform        block,    -   a variable cIdx specifying the colour component of the current        block,    -   an (nTbW)×(nTbH) array d[x][y] of scaled transform coefficients        with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

Output of this process is the (nTbW)×(nTbH) array r[x][y] of residualsamples with x=0 . . . nTbW−1, y=0 . . . nTbH−1.

If cu_sbt_flag[xTbY][yTbY] is equal to 1, the variable trTypeHorspecifying the horizontal transform kernel and the variable trTypeVerspecifying the vertical transform kernel are derived in Table 8-Xdepending on cu_sbt_horizontal_flag[xTbY][yTbY] andcu_sbt_pos_flag[xTbY][yTbY].

Otherwise (cu_sbt_flag[xTbY][yTbY] is equal to 0), the variabletrTypeHor specifying the horizontal transform kernel and the variabletrTypeVer specifying the vertical transform kernel are derived in Table8-9 depending on mts_idx[xTbY][yTbY] and CuPredMode[xTbY][yTbY].

The (nTbW)×(nTbH) array r of residual samples is derived as follows:

(1) Each (vertical) column of scaled transform coefficients d[x][y] withx=0 . . . nTbW−1, y=0 . . . nTbH−1 is transformed to e[x][y] with x=0 .. . nTbW−1, y=0 . . . nTbH−1 by invoking the one-dimensionaltransformation process for each column x=0 . . . nTbW−1 with the heightof the transform block nTbH, the list d[x][y] with y=0 . . . nTbH−1 andthe transform type variable trType set equal to trTypeVer as inputs, andthe output is the list e[x][y] with y=0 . . . nTbH−1.

(2) The intermediate sample values g[x][y] with x=0 . . . nTbW−1, y=0 .. . nTbH−1 are derived as follows:g[x][y]=Clip3(CoeffMin,CoeffMax,(e[x][y]+256)>>9)  (8-393)

(3) Each (horizontal) row of the resulting array g[x][y] with x=0 . . .nTbW−1, y=0 . . . nTbH−1 is transformed to r[x][y] with x=0 . . .nTbW−1, y=0 . . . nTbH−1 by invoking the one-dimensional transformationprocess for each row y=0 . . . nTbH−1 with the width of the transformblock nTbW, the list g[x][y] with x=0 . . . nTbW−1 and the transformtype variable trType set equal to trTypeHor as inputs, and the output isthe list r[x][y] with x=0 . . . nTbW−1.

TABLE 10 Specification of trTypeHor and trTypeVer depending on mts_idx[x ][ y ] and CuPredMode[ x ][ y ] cu_sbt_horizontal_flagcu_sbt_horizontal_flag [ xTbY ][ yTbY ] = = 0 [ xTbY ][ yTbY ] = = 1cu_sbt_pos_flag cu_sbt_pos_flag cu_sbt_pos_flag cu_sbt_pos_flag [ xTbY][ yTbY ] = = 0 [ xTbY ][ yTbY ] = = 1 [ xTbY ][ yTbY ] = = 0 [ xTbY ][yTbY ] = = 1 trTypeHor 2 1 nTbW > 32 ? 0 : 1 nTbW > 32 ? 0 : 1 trTypeVernTbH > 32 ? 0 : 1 nTbH > 32 ? 0 : 1 2 1

TABLE 11 Specification of trTypeHor and trTypeVer depending on mts idx[x ][ y ] and CuPredMode[ x ][ y ] CuPredMode[ xTbY ][ yTbY ] ==MODE_INTRA CuPredMode[ xTbY ][ xTbY ] == MODE_INTER mts_idx[ xTbY ][yTbY ] trTypeHor trTypeVer trTypeHor trTypeVer −1 (inferred) 0 0 0 0 0(00) 1 1 2 2 1 (01) 2 1 1 2 2 (10) 1 2 2 1 3 (11) 2 2 1 1

In current VVC draft, there is a limitation on the maximum transformunit, which is 64×64. If the CU width (W) or height (H) is greater than64, then the CU is implicitly split into multiples ofmin(W,64)×min(H,64) sub-blocks, and transform is performed on eachsub-blocks, namely sub transform unit (STU).

In JVET-N0362 and a previous provisional application by the inventors, aconfigurable max transform size scheme is proposed. The proposed methodallows an alternative maximum transform size smaller than 64-length. Forexample, when the maximum transform size is set as 16, and the CU width(W) or height (H) is greater than 16, the CU is implicitly split intomultiples of min(W,16)×min(H,16) sub-blocks, and transform is performedon each sub-blocks, namely sub transform unit (STU). In addition, thewidth and height of STU cannot be greater than the max transform size.

However, there are several disadvantages in the above described methods.For example, when the coding unit is split into multiple STUs, typicallythere can be correlation among the DC values of these STUs. But thesecorrelations are not considered in the current VCC draft for codingperformance improvement. In addition, in current VVC draft, thesignaling of MTS and Transform skip is operated in TU level, therefore alarge CU may still apply and signal MTS and transform skip for each STU,which may be inefficient.

According to the embodiments of the present disclosure, methods forpredicting the DC values applied in sub transform unit are provided. Thedisclosed methods can be used separately or combined in any order.Further, each of the methods (or embodiments), encoder, and decoder maybe implemented by processing circuitry (e.g., one or more processors orone or more integrated circuits). In one example, the one or moreprocessors execute a program that is stored in a non-transitorycomputer-readable medium.

According to some embodiments, a high-level syntax (HLS) element canrefer to any of Video Parameter Set (VPS), Sequence Parameter Set (SPS),Picture Parameter Set (PPS), Slice header, Tile header, Tile groupheader. A CTU (coding tree unit, which is the largest CU size) headerrefers to syntax elements signaled for each CTU, e.g., as headerinformation. A transform size refers to the maximum transform widthand/height, or maximum transform unit area size. A low-frequencycoefficient (LFC) can refer to only DC coefficient, or the two (orthree) coefficients which are closest to DC coefficient, or the top-leftm×n transform coefficients (or spatial residuals in case transform skipis applied), or a pre-defined region of transform coefficients (orspatial residuals in case transform skip is applied) in the top-left M×Npart of coefficient block.

In an embodiment, the disclosed method includes signaling an HLS toindicate whether an additional transform type other than DCT-2 isapplied. When a flag sps_enable_dst7_flag, or sps_enable_dst7_dct8_flagis true, a DST-7, or DCT-8 can be applied during the transformation.When the flag sps_enable_dst7_flag and sps_enable_dst7_dct8_flag arefalse, in an example, an HLS is signaled to indicate whether only DCT-2or Transform skip can be applied. In an example, an HLS is signaled toindicate whether only DCT-2 can be applied.

In an embodiment, the MTS and/or the Transform Skip is not signaled if aCU is implicitly split into multiple STUs.

In an embodiment, when a current CU is split into multiples of STU, foreach of the STUs, the absolute values of LFC, or the sign values (alsoreferred to as signed values) of LFC, can be predicted using thecoefficients of neighboring blocks, and/or neighboring STUs. Forexample, as shown in FIG. 12, a 64×32 CU is split to eight 16×16 STUswhen the maximum transform size is set to 16-length, for the current STU(C), the LFC of the top STU (T) and the left STU (L) and top-leftSTU(TL), can be used to predict the absolute value or sign value (alsoreferred to as signedvalue) of current STU.

In a first example, the absolute value of LFC of a current STU ispredicted using the average (or the median value) of the absolute valuesof DC coefficients of the top and/or left neighboring blocks (orsub-blocks, STUs). For example, DC_(C)=(DC_(T)+DC_(L)+1)/(2*N), where Nis a positive integer. In one embodiment, N=1. In another embodiment,N=2.

In a second example, the absolute value of LFC of a current STU ispredicted using the average of the absolute values of LFC of the top andleft neighboring blocks (or sub-blocks, STUs) which belongs to the sameCU.

In a third example, the absolute value of LFC of a current STU ispredicted using the absolute values LFC of the top and left neighboringblocks and not coded by Transform Skip mode.

In a fourth example, the absolute value of LFC of current STU ispredicted using the absolute values LFC of the top and left neighboringblocks which are (is) coded using the same transform type (e.g., DCT-2,DST-7 or DCT-8).

In a fifth example, if the current STU and a neighboring block are codedusing different transform types, e.g., the current STU is coded by DCT-2and neighboring block is coded by Transform Skip, then the absolutevalue of LFC of this neighboring STU is scaled before being used forpredicting the LFC of current block. The scale factor may be √{squareroot over (2)} or 1/√{square root over (2)} or m/2^(N), where m and Nare integers.

In a sixth example, the sign value of LFC of current STU is predictedusing the average (or the median value) of the sign values of the topand/or left neighboring blocks after rounding to the nearest integer.For example, when three neighboring blocks are used for predicting thesign values, the sign value of a current block is predicted using thesign value which appeared 2 or more times in the neighboring block.

In a seventh example, the sign value of LFC of current STU is predictedusing the average of the sign values of the top and left neighboringblocks which belongs to the same CU.

In a eighth example, the sign value (also referred to as signed value)of LFC of current STU is predicted using the sign value LFC of the topand left neighboring blocks which are (is) not coded by Transform Skipmode.

In a ninth example, the sign value of LFC of current STU is predictedusing the sign value LFC of the top and left neighboring blocks whichare (is) coded using the same transform type (e.g., DCT-2, DST-7 orDCT-8).

According to some embodiments, the methods mentioned above from thefirst example to the ninth example can be applied to STUs generated bysub-partitions of ISP mode, or STUs generated by an implicit transformsplit. The methods mentioned above can also be performed on quantizedcoefficients or dequantized coefficients.

In an embodiment, when the current CU is split into multiple of STUs, asecondary transform can be applied on a block (or coefficient block)which is composed by the LFCs of the STUs. For example, as shown in FIG.13, a 32×64 block (or CU) is split into eight 16×16 STUs, the DCcoefficients of each STU (e.g., textured block located at the top-leftof each STU) are identified and construct a new 4×2 block (orcoefficient block), and a secondary transform can be performed on this4×2 block.

In an example, the transform coefficients of the secondary transform canbe fed back to a corresponding LFC of STUs. In another example, thetransform coefficients of the secondary transform can be codedseparately as a coefficient block.

In an example, the secondary transform can be a non-square Hadamardtransform. Examples include, 2×4, 1×4, 4×2, 4×1, 2×8, 8×2, etc. In anexample, the secondary transform can be a square Hadamard transform. Inan example, the secondary transform can be a DCT-2. In an example, thesecondary transform can be a DST-7 or DCT-8. In an example, thesecondary transform can be a Karhunen-Loeve Transform (KLT), or anon-separable transform (e.g., a non-separable KLT).

In an example, a dimension of the secondary transform can be alignedwith the number of STUs along the horizontal and vertical directions.

In an example, the secondary transform is applied only when all STUs ofthe CU share the same transform type.

In an example, different secondary transforms can be applied. The typeof secondary transform is determined based on the primary transform ofSTUs.

In current VCC draft, when the coding unit is split into multiple STUs,typically there can be correlation among the DC values of these STUs.But these correlations are not considered in the current VCC draft forcoding performance improvement. In addition, in current VVC draft, thesignaling of MTS and Transform skip is operated in TU level, therefore alarge CU may still apply and signal MTS and transform skip for each STU,which may be inefficient. In the present disclosure, methods forpredicting the DC values applied in sub transform units are provided. Inthe disclosed methods, a low frequency coefficient (or DC value) of acurrent transform unit can be determined based on the transform type andlow frenquency coefficients of neighboring sub transform units, which inturn gains the coding efficiency.

FIG. 14 shows a flow chart outlining a process (1400) according to anembodiment of the disclosure. The process (1400) can be used in thereconstruction of a block coded in intra mode, so to generate aprediction block for the block under reconstruction. In variousembodiments, the process (1400) are executed by processing circuitry,such as the processing circuitry in the terminal devices (110), (120),(130) and (140), the processing circuitry that performs functions of thevideo encoder (203), the processing circuitry that performs functions ofthe video decoder (210), the processing circuitry that performsfunctions of the video decoder (310), the processing circuitry thatperforms functions of the video encoder (403), and the like. In someembodiments, the process (1400) is implemented in software instructions,thus when the processing circuitry executes the software instructions,the processing circuitry performs the process (1400). The process startsat (S1401) and proceeds to (S1410).

At (S1410), transform block signaling information is acquired from acoded video bitstream. The transform block signaling information can bea first high level syntax element that indicates the transform type is adiscrete cosine transform 2 (DCT-2), a second high level syntax elementthat indicates the transform type is one of the DCT-2 or a transformskip, or a third high level syntax element that indicates the transformtype is a multiple transform selection (MTS) based on a discrete cosinetransform 8 (DCT-8) and a discrete sine transform 7 (DST-7).

At (S1420), a transform type can be determined based on the transformblock signaling information. As mentioned above, the transform type canbe a DCT-2, a transform skip, a DST-7, or a DCT-8 according to thetransform block signaling information.

At (S1430), a low frequency coefficient of one of a plurality of subtransform units is determined based on the transform type andneighboring sub transform units of the one of the plurality of subtransform units, where the plurality of sub transform units arepartitioned from a current coding block unit (CU).

In some embodiments, an absolute value or a signed value of the lowfrequency coefficient of the one of the plurality of sub transform unitscan be determined based on transform coefficients of the neighboring subtransform units of the one of the plurality of sub transform units.

At (S1440), the current coding block unit is encoded based on the lowfrequency coefficients of the plurality of sub transform units.

In some embodiments, a secondary transform is performed on the lowfrequency coefficients of the plurality of sub transform units to obtaina plurality of transform coefficients. Each of the plurality oftransform coefficients is obtained based on a corresponding lowfrequency coefficient of the plurality of sub transform units. Thecurrent coding block unit can be decoded based on the plurality oftransform coefficients. In an example, the transform coefficients of thesecondary transform can be fed back to the corresponding LFC of STUs. Inanother example, the transform coefficients of the secondary transformcan be encoded separately as a coefficient block.

The techniques described above, can be implemented as computer softwareusing computer-readable instructions and physically stored in one ormore computer-readable media. For example, FIG. 15 shows a computersystem (1500) suitable for implementing certain embodiments of thedisclosed subject matter.

The computer software can be coded using any suitable machine code orcomputer language, that may be subject to assembly, compilation,linking, or like mechanisms to create code comprising instructions thatcan be executed directly, or through interpretation, micro-codeexecution, and the like, by one or more computer central processingunits (CPUs), Graphics Processing Units (GPUs), and the like.

The instructions can be executed on various types of computers orcomponents thereof, including, for example, personal computers, tabletcomputers, servers, smartphones, gaming devices, internet of thingsdevices, and the like.

The components shown in FIG. 15 for computer system (1500) are exemplaryin nature and are not intended to suggest any limitation as to the scopeof use or functionality of the computer software implementingembodiments of the present disclosure. Neither should the configurationof components be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary embodiment of a computer system (1500).

Computer system (1500) may include certain human interface inputdevices. Such a human interface input device may be responsive to inputby one or more human users through, for example, tactile input (such as:keystrokes, swipes, data glove movements), audio input (such as: voice,clapping), visual input (such as: gestures), olfactory input (notdepicted). The human interface devices can also be used to capturecertain media not necessarily directly related to conscious input by ahuman, such as audio (such as: speech, music, ambient sound), images(such as: scanned images, photographic images obtain from a still imagecamera), video (such as two-dimensional video, three-dimensional videoincluding stereoscopic video).

Input human interface devices may include one or more of (only one ofeach depicted): keyboard (1501), mouse (1502), trackpad (1503), touchscreen (1510), data-glove (not shown), joystick (1505), microphone(1506), scanner (1507), camera (1508).

Computer system (1500) may also include certain human interface outputdevices. Such human interface output devices may be stimulating thesenses of one or more human users through, for example, tactile output,sound, light, and smell/taste. Such human interface output devices mayinclude tactile output devices (for example tactile feedback by thetouch-screen (1510), data-glove (not shown), or joystick (1505), butthere can also be tactile feedback devices that do not serve as inputdevices), audio output devices (such as: speakers (1509), headphones(not depicted)), visual output devices (such as screens (1510) toinclude CRT screens, LCD screens, plasma screens, OLED screens, eachwith or without touch-screen input capability, each with or withouttactile feedback capability—some of which may be capable to output twodimensional visual output or more than three dimensional output throughmeans such as stereographic output; virtual-reality glasses (notdepicted), holographic displays and smoke tanks (not depicted)), andprinters (not depicted).

Computer system (1500) can also include human accessible storage devicesand their associated media such as optical media including CD/DVD ROM/RW(1520) with CD/DVD or the like media (1521), thumb-drive (1522),removable hard drive or solid state drive (1523), legacy magnetic mediasuch as tape and floppy disc (not depicted), specialized ROM/ASIC/PLDbased devices such as security dongles (not depicted), and the like.

Those skilled in the art should also understand that term “computerreadable media” as used in connection with the presently disclosedsubject matter does not encompass transmission media, carrier waves, orother transitory signals.

Computer system (1500) can also include an interface to one or morecommunication networks. Networks can for example be wireless, wireline,optical. Networks can further be local, wide-area, metropolitan,vehicular and industrial, real-time, delay-tolerant, and so on. Examplesof networks include local area networks such as Ethernet, wireless LANs,cellular networks to include GSM, 3G, 4G, 5G, LTE and the like, TVwireline or wireless wide area digital networks to include cable TV,satellite TV, and terrestrial broadcast TV, vehicular and industrial toinclude CANBus, and so forth. Certain networks commonly require externalnetwork interface adapters that attached to certain general purpose dataports or peripheral buses (1549) (such as, for example USB ports of thecomputer system (1500)); others are commonly integrated into the core ofthe computer system (1500) by attachment to a system bus as describedbelow (for example Ethernet interface into a PC computer system orcellular network interface into a smartphone computer system). Using anyof these networks, computer system (1500) can communicate with otherentities. Such communication can be uni-directional, receive only (forexample, broadcast TV), uni-directional send-only (for example CANbus tocertain CANbus devices), or bi-directional, for example to othercomputer systems using local or wide area digital networks. Certainprotocols and protocol stacks can be used on each of those networks andnetwork interfaces as described above.

Aforementioned human interface devices, human-accessible storagedevices, and network interfaces can be attached to a core (1540) of thecomputer system (1500).

The core (1540) can include one or more Central Processing Units (CPU)(1541), Graphics Processing Units (GPU) (1542), specialized programmableprocessing units in the form of Field Programmable Gate Areas (FPGA)(1543), hardware accelerators for certain tasks (1544), and so forth.These devices, along with Read-only memory (ROM) (1545), Random-accessmemory (1546), internal mass storage such as internal non-useraccessible hard drives, SSDs, and the like (1547), may be connectedthrough a system bus (1548). In some computer systems, the system bus(1548) can be accessible in the form of one or more physical plugs toenable extensions by additional CPUs, GPU, and the like. The peripheraldevices can be attached either directly to the core's system bus (1548),or through a peripheral bus (1549). Architectures for a peripheral businclude PCI, USB, and the like.

CPUs (1541), GPUs (1542), FPGAs (1543), and accelerators (1544) canexecute certain instructions that, in combination, can make up theaforementioned computer code. That computer code can be stored in ROM(1545) or RAM (1546). Transitional data can be also be stored in RAM(1546), whereas permanent data can be stored for example, in theinternal mass storage (1547). Fast storage and retrieve to any of thememory devices can be enabled through the use of cache memory, that canbe closely associated with one or more CPU (1541), GPU (1542), massstorage (1547), ROM (1545), RAM (1546), and the like.

The computer readable media can have computer code thereon forperforming various computer-implemented operations. The media andcomputer code can be those specially designed and constructed for thepurposes of the present disclosure, or they can be of the kind wellknown and available to those having skill in the computer software arts.

As an example and not by way of limitation, the computer system havingarchitecture (1500), and specifically the core (1540) can providefunctionality as a result of processor(s) (including CPUs, GPUs, FPGA,accelerators, and the like) executing software embodied in one or moretangible, computer-readable media. Such computer-readable media can bemedia associated with user-accessible mass storage as introduced above,as well as certain storage of the core (1540) that are of non-transitorynature, such as core-internal mass storage (1547) or ROM (1545). Thesoftware implementing various embodiments of the present disclosure canbe stored in such devices and executed by core (1540). Acomputer-readable medium can include one or more memory devices orchips, according to particular needs. The software can cause the core(1540) and specifically the processors therein (including CPU, GPU,FPGA, and the like) to execute particular processes or particular partsof particular processes described herein, including defining datastructures stored in RAM (1546) and modifying such data structuresaccording to the processes defined by the software. In addition or as analternative, the computer system can provide functionality as a resultof logic hardwired or otherwise embodied in a circuit (for example:accelerator (1544)), which can operate in place of or together withsoftware to execute particular processes or particular parts ofparticular processes described herein. Reference to software canencompass logic, and vice versa, where appropriate. Reference to acomputer-readable media can encompass a circuit (such as an integratedcircuit (IC)) storing software for execution, a circuit embodying logicfor execution, or both, where appropriate. The present disclosureencompasses any suitable combination of hardware and software.

APPENDIX A: ACRONYMS

-   JEM: joint exploration model-   VVC: versatile video coding-   BMS: benchmark set-   MV: Motion Vector-   HEVC: High Efficiency Video Coding-   SEI: Supplementary Enhancement Information-   VUI: Video Usability Information-   GOPs: Groups of Pictures-   TUs: Transform Units,-   PUs: Prediction Units-   CTUs: Coding Tree Units-   CTBs: Coding Tree Blocks-   PBs: Prediction Blocks-   HRD: Hypothetical Reference Decoder-   SNR: Signal Noise Ratio-   CPUs: Central Processing Units-   GPUs: Graphics Processing Units-   CRT: Cathode Ray Tube-   LCD: Liquid-Crystal Display-   OLED: Organic Light-Emitting Diode-   CD: Compact Disc-   DVD: Digital Video Disc-   ROM: Read-Only Memory-   RAM: Random Access Memory-   ASIC: Application-Specific Integrated Circuit-   PLD: Programmable Logic Device-   LAN: Local Area Network-   GSM: Global System for Mobile communications-   LTE: Long-Term Evolution-   CANBus: Controller Area Network Bus-   USB: Universal Serial Bus-   PCI: Peripheral Component Interconnect-   FPGA: Field Programmable Gate Areas-   SSD: solid-state drive-   IC: Integrated Circuit-   CU: Coding Unit

While this disclosure has described several exemplary embodiments, thereare alterations, permutations, and various substitute equivalents, whichfall within the scope of the disclosure. It will thus be appreciatedthat those skilled in the art will be able to devise numerous systemsand methods which, although not explicitly shown or described herein,embody the principles of the disclosure and are thus within the spiritand scope thereof.

What is claimed is:
 1. A method for video decoding in a decoder,comprising: acquiring, with processing circuitry of the decoder,transform block signaling information from a coded video bitstream;determining, with the processing circuitry of the decoder, a transformtype based on the transform block signaling information; determining,with the processing circuitry of the decoder, a low frequencycoefficient of one of a plurality of sub transform units based on thetransform type and neighboring sub transform units of the one of theplurality of sub transform units, the plurality of sub transform unitsbeing partitioned from a current coding block unit (CU); and decoding,with the processing circuitry of the decoder, the current coding blockunit (CU) based on low frequency coefficients of the plurality of subtransform units, the low frequency coefficients including the lowfrequency coefficient of the one of the plurality of sub transformunits, wherein the determining of the low frequency coefficient includesat least determining a signed value of the low frequency coefficient ofthe one of the plurality of sub transform units based on an average ofsigned values of low frequency coefficients of at least one of a topneighboring sub transform unit and a left neighboring sub transform unitof the one of the plurality of sub transform units.
 2. The method ofclaim 1, wherein the transform block signaling information is one of afirst high level syntax element that indicates the transform type is adiscrete cosine transform 2 (DCT-2); a second high level syntax elementthat indicates the transform type is one of the DCT-2 or a transformskip; and a third high level syntax element that indicates the transformtype is a multiple transform selection (MTS) based on a discrete cosinetransform 8 (DCT-8) and a discrete sine transform 7 (DST-7).
 3. Themethod of claim 1, wherein the transform block signaling informationindicates that the transform type is a discrete cosine transform 2(DCT-2) responsive to the plurality of sub transform units beingpartitioned from the current coding block unit (CU) by an implicittransform split.
 4. The method of claim 1, wherein the determining thelow frequency coefficient further comprises: determining an absolutevalue of the low frequency coefficient of the one of the plurality ofsub transform units based on transform coefficients of the neighboringsub transform units of the one of the plurality of sub transform units.5. The method of claim 4, further comprising: determining the absolutevalue of the low frequency coefficient of the one of the plurality ofsub transform units based on an average of absolute values of lowfrequency coefficients of at least one of the top neighboring subtransform unit and the left neighboring sub transform unit of the one ofthe plurality of sub transform units.
 6. The method of claim 4, whereinabsolute values of low frequency coefficients of neighboring subtransform units are scaled, responsive to the one of the plurality ofsub transform units and the neighboring sub transform units of the oneof the plurality of sub transform units being transformed based ondifferent transform types.
 7. The method of claim 4, wherein theplurality of sub transform units are partitioned from the current codingblock unit based on at least one of an Intra Sub-Partitions mode, or animplicit transform split.
 8. The method of claim 1, after the lowfrequency coefficient of the one of the plurality of sub transform unitsis determined, the method further comprising: performing a secondarytransform on the low frequency coefficients of the plurality of subtransform units to obtain a plurality of transform coefficients, each ofthe plurality of transform coefficients being obtained based on acorresponding low frequency coefficient of the plurality of subtransform units, wherein the decoding includes decoding the currentcoding block unit based on the plurality of transform coefficients. 9.The method of claim 8, wherein the secondary transform is one of anon-square Hadamard transform, a square Hadamard transform, a DCT-2, aDST-7, a DCT-8, a Karhunen-Loeve Transform (KLT), or a non-separableKLT.
 10. The method of claim 8, wherein the secondary transform isperformed responsive to the plurality of sub transform units in thecurrent coding block unit (CU) sharing a same transform type.
 11. Anapparatus for video decoding, comprising: processing circuitryconfigured to: acquire transform block signaling information from acoded video bitstream; determine a transform type based on the transformblock signaling information; determine a low frequency coefficient ofone of a plurality of sub transform units based on the transform typeand neighboring sub transform units of the one of the plurality of subtransform units, the plurality of sub transform units being partitionedfrom a current coding block unit (CU); and decode the current codingblock unit based on low frequency coefficients of the plurality of subtransform units, the low frequency coefficients including the lowfrequency coefficient of the one of the plurality of sub transformunits, wherein to determine the low frequency coefficient, theprocessing circuitry at least determines a signed value of the lowfrequency coefficient of the one of the plurality of sub transform unitsbased on an average of signed values of low frequency coefficients of atleast one of a top neighboring sub transform unit and a left neighboringsub transform unit of the one of the plurality of sub transform units.12. The apparatus of claim 11, wherein the transform block signalinginformation is one of a first high level syntax element that indicatesthe transform type is a discrete cosine transform 2 (DCT-2); a secondhigh level syntax element that indicates the transform type is one ofthe DCT-2 or a transform skip; and a third high level syntax elementthat indicates the transform type is a multiple transform selection(MTS) based on a discrete cosine transform 8 (DCT-8) and a discrete sinetransform 7 (DST-7).
 13. The apparatus of claim 11, wherein thetransform block signaling information indicates that the transform typeis a discrete cosine transform 2 (DCT-2) responsive to the plurality ofsub transform units being partitioned from the current coding block unit(CU) by an implicit transform split.
 14. The apparatus of claim 11,wherein the processing circuitry is further configured to: determine anabsolute value of the low frequency coefficient of the one of theplurality of sub transform units based on transform coefficients of theneighboring sub transform units of the one of the plurality of subtransform units.
 15. The apparatus of claim 14, wherein the processingcircuitry is further configured to determining the absolute value of thelow frequency coefficient of the one of the plurality of sub transformunits based on an average of absolute values of low frequencycoefficients of at least one of the top neighboring sub transform unitand the left neighboring sub transform unit of the one of the pluralityof sub transform units.
 16. The apparatus of claim 14, wherein absolutevalues of low frequency coefficients of neighboring sub transform unitsare scaled responsive to the one of the plurality of sub transform unitsand the neighboring sub transform units being transformed based ondifferent transform types.
 17. The apparatus of claim 14, wherein theplurality of sub transform units are partitioned from the current codingblock unit based on at least one of an Intra Sub-Partitions (ISP) mode,or an implicit transform split.
 18. The apparatus of claim 11, theprocessing circuitry is configured to: perform a secondary transform onthe low frequency coefficients of the plurality of sub transform unitsto obtain a plurality of transform coefficients, each of the pluralityof transform coefficients being obtained based on a corresponding lowfrequency coefficient of the plurality of sub transform units; anddecode the current coding block unit based on the plurality of transformcoefficients.
 19. The apparatus of claim 18, wherein the secondarytransform is one of a non-square Hadamard transform, a square Hadamardtransform, a DCT-2, a DST-7, a DCT-8, a Karhunen-Loeve Transform (KLT),or a non-separable KLT.
 20. A non-transitory computer-readable mediumstoring instructions which when executed by a computer for videodecoding cause the computer to perform: acquiring transform blocksignaling information from a coded video bitstream; determining atransform type based on the transform block signaling information;determining a low frequency coefficient of one of a plurality of subtransform units based on the transform type and neighboring STUs of theone of the plurality of sub transform units, the plurality of subtransform units being partitioned from a current coding block unit (CU);and decoding the current coding block unit based on low frequencycoefficients of the plurality of sub transform units, the low frequencycoefficients including the low frequency coefficient of the one of theplurality of sub transform units, wherein the determining of the lowfrequency coefficient includes at least determining a signed value ofthe low frequency coefficient of the one of the plurality of subtransform units based on an average of signed values of low frequencycoefficients of at least one of a top neighboring sub transform unit anda left neighboring sub transform unit of the one of the plurality of subtransform units.